Well, it's the pleasure to be talking here at home, of course, and I'm very glad to have this opportunity. And so I'm going to start by talking about something that says in the title. It says I'm going to talk about robust dynamical properties. So by robust, and in general, every time I'm talking about the topology in which I am looking at the flows, I'm always going to be talking about the C1 topology. Okay, so when I say robust, what I mean is a property that is held by an open set of vector fields or the theomorphisms. And when I say open set, I mean C1. Of course, you can make the definition for CR, but for this talk it's going to be, well, this doesn't work. CR, you can make the definition for CR, but for this talk it's going to be C1. Okay, and so the idea is to try to find ways to understand when a property is robust by looking at only one vector field or the theomorphism. Okay, for example, if you think about one property that's held by a whole open set of systems, like having all the periodic orbits hyperbolic for all the systems in the neighborhood, you would like to be able to detect this by only looking at one system. Also, there is some idea that if a property is persistent by perturbations, by C1 perturbations, there should be something in the structure of the vector fields that have this property that doesn't allow for big bifurcations by perturbations. So that's more or less the idea. And well, when I say that I want to look at dynamical properties, I'm not going to be looking at dynamical properties that are for all the orbits in the whole manifold. I'm just going to be focused on some particular orbits, which are the ones that are important for me, which are the recurrent ones. In this case, we are going to be looking at the chain recurrent classes, which are... So the points that can be... So one point is chain recurrent. If you can go from it back to itself by an epsilon to the orbit, which epsilon to the orbit is going to be to allow to have a mistake every time you make a step in the orbit. So you make one iteration, you can have an epsilon mistake, then you make one iteration and like that. So the points that are chain recurrents are the ones that you can come back to itself by doing this iteration. So one example, and this reminds me a bit of Enrique's talk, because I'm going to be talking about this, which is called dominated splitting, and it's one of my yes toys. So this is an example of what I say when I say I want to look at an open... I want to look at one system and detect a property that's held by a neighborhood of systems. So that picture there, supposed to show a dominated splitting in drawing wise, because I don't want to be too precise, but essentially it's that you would have along an orbit, or you would have a splitting of the tangent space. And this splitting is in a way that if you wait some time, the vectors in one of the spaces are less expanded than the vectors in another space. And you, in the other space. And you can detect this because you can see a cone field around one of the spaces that gets... when you iterate, the cone gets inside itself. And so the space that dominates is the one that is inside all the cones when you iterate. And the vectors that never get inside of one of these cones is the other space. So that will be more or less an idea of what is a dominated splitting. And if you look at this property by looking at the ideas of the cones, you can more or less get the feeling that this actually is a robust property. Because, well, the property of having cones that get inside each other is something that doesn't change much if you change the derivative very little. So this is an example of a property that is robust, but that you can detect only by looking at one system. Okay, so the dominated splitting is a robust property. You can always find, I said this was a splitting of the tangent space, and you can do it in the finest way. You can find the finest possible way of splitting the tangent space into spaces that behave in that way. And, well, so I start with dominated splitting and the relationship with robust properties because if you don't have a dominated splitting, you don't have robustness of properties. So this is a property that you can detect by looking at one system. And if this system has it, okay, then all the systems nearby have this robust property. But if this system doesn't have this property, then the neighbors don't have any shared property that you can say. So the idea now is to ask a little bit more than dominated splitting. Because as a robust property, this is very weak. I say this is an obstruction for getting all the other robust properties. But I would like to understand a little bit what other things I can ask of a vector field that make more precise other robust properties or the other way around which robust properties imply in the vector fields of my neighborhood some structure on the tangent space. So there's these two ways. And so the hyperbolic structures is what I'm going to be looking at. I'm going to be trying to find hyperbolic structures which are my way of trying to understand when a robust property is there or when it's not. And every time I say a hyperbolic structure, I will mean this. I will mean that there is a dominated splitting. And I will mean that this is valid for vector fields or for defiomorphisms. But when I look at the tangent space and I look at this splitting, I will look at the Jacobian of the vector field or the defiomorphism. And so what I want to try to find is when there is a subspace of one of the spaces in my splitting of the dominated splitting, that when I look at the Jacobian restricted to the subspace, I see a contraction or an expansion of vectors or of the volume of something, of the Jacobian. So I look at the Jacobian and I look at the subspaces of my splitting. And I want to see if in any of these cases I can find a contraction or an expansion. This would be a hyperbolic structure. And I'm going to be trying to talk about the relationship of these things with the robust properties. Okay, so in the case where, for example, the subspace that I'm looking at is one dimensional, what you're looking at when you say the expansion or contraction of the Jacobian, you're actually talking about expansion or contraction of vectors. And in this case what you get is hyperbolicity. So what you would have is that for any one dimensional subspace, for example, of the stable space, the Jacobian, which in this case is just the derivative on the vector, is contracted and in the other case expanded. So you can also do other definitions of this kind. For example, partial hyperbolicity, where you see contraction of vectors in the stable space, expansion of vectors in the unstable space, and something in between in the other space. So you're not asking the contraction in all the subspaces of the splitting, but just on the ones in the sides. Well, there's this other which is called volume partial hyperbolicity, which is more, you understand a little bit more why I was talking about the Jacobian of the lab, because in the other case was just contraction and expansion of vectors. In this case, what you're asking is that the extremal bundles, which are the ones that are more in the sides, contract or expand volume. And why am I talking about this? Well, because there is a relationship between this kind of hyperbolicities, hyperbolic structures, and the robustness of properties. One of them was, the one was largely discussed yesterday, which is the C1 stability conjecture, which actually says, okay, hyperbolicity implies that you will keep all your dynamical properties in your recurrent set. And also the other way around, the fact that you keep all the dynamical properties of your vector field or whatever in a neighborhood, this forces you to have some structure in the tangent space. But there are other weaker results like this one, for example, which is, okay, if you have a robust intransitivity or robust transitivity, it depends if you are talking about all of them or an open-ended set, this forces also some structure in the tangent space. So these are examples of the kind of things I'm looking at. Relationship between having something that's persistent and some structure that is forced on the vector fields that have this property and the other way around. Well, these results that I was saying here, they are for different morphisms. The C1 stability conjecture and this one, which is the robust transitivity implies volume partial hyperbolicity. And so I was wondering what happens with flows. And the thing with flows is that some of the results are more or less easy to keep when you don't have singularities. Others just don't. And the development of these kinds of relationships between one thing and the other, it's at least developing slower than in the case of the theomorphisms. So if you try to do a direct generalization of the results of the theomorphisms for flows, you don't get what you want, essentially. So as I said, for the theomorphisms, we have this property that if you don't have dominant splitting, then you don't get robust properties of anything. But this is not true for the theomorphisms. You can have a robustly transitive set and not have dominated splitting of the tangent space. And also, again, related to the C1 stability conjecture, as was also explained yesterday, one step to prove the stability conjecture is to think, okay, I have the theomorphism which is hyperbolic. Then I have a lot of stuff in between, but then I have periodic orbits that are hyperbolic for this theomorphism and for the surrounding the theomorphisms. Okay, but then I'm stable. So there is this middle step that's there which talks about the persistence of the hyperbolicity of the periodic orbits. And this is supposed to imply hyperbolicity and it's supposed to imply stability. But this is not true for flows. There are examples of things that have all the periodic orbits robustly hyperbolic, but that they are not stable because when you do a perturbation in flows there are other ways of killing periodic orbits which is not losing the hyperbolicity. So as a matter, just to make some idea of what I'm talking about, suppose you have a singularity like this of a flow and you have a homoclinic connection, then you can have periodic orbits that are every time more near the homoclinic connection. These periodic orbits can be hyperbolic because, well, whatever behavior is in the periodic orbit is mostly dominated by the time it spends near the singularity and if the singularity is hyperbolic then you can inherit this. Suppose this is pre-dimensional, of course, to the periodic orbit, so the periodic orbit will be hyperbolic, but then you can make a small perturbation and make the periodic orbit converge to the cycle and then you lose the periodic orbit and you never lose the hyperbolicity in this process. So there are new phenomena happening in flows that don't happen in the theomorphisms which make this connection more complicated. In the other case, in the case of robust transitivity and the dominated splitting, the problem is another, the problem is that in your tangent space you have something occupying some space which is the direction of the flow. This doesn't exist in the theomorphisms. So the direction of the flow is playing a role in the splitting of your tangent space and this complicates finding a splitting because if you approach, if you have orbits that are almost tangent to the direction where you're supposed to expand more and then get almost tangent to the direction where you're supposed to contract more then you start mixing the dominated splitting just because there is a problem with the direction of the flow and this doesn't happen in the theomorphisms so you don't have this problem and you can make your theory in peace but you have to deal with this when you are talking about flows. So there's been a lot of work in trying to solve these kind of problems. There are some things about the singularities and there are other things about the dominated splitting of things when there are no singularities. So essentially you have two ways of dealing with these kind of problems. One is when you have singularities and the other one is when you don't have singularities. So when you have singularities one of the problems that I mentioned about the singularities was the possibility of losing periodic orbits by preservation so we still want to try to find some structure in the tangent space that has some relation with the fact that the periodic orbits are all the time robustly hyperbolic. So we want to find some relationship of this sort because there is a really big persistence of something and you want to detect it. Okay, so one attempt of trying to find a structure for these kind of systems is this one which works in lower dimension which is to try to find, okay, it's not hyperbolic when you have periodic orbits of when the periodic orbits are robustly hyperbolic you don't get hyperbolicity but could you maybe find a weaker hyperbolic structure. And well, this works very well in low dimension and the idea is, as I will explain, this is the definition of singular hyperbolicity which appears in Morales Pacifico Pujals work and it works very well in various settings as a way of fixing this problem. So you have the singularity and you don't have a black pencil here. You have the singularity and then you have periodic orbits that approach the singularity. So with green. The splitting of the tangent space of the periodic orbit which we suppose is hyperbolic is of this kind. Yes, times, suppose we are in dimension 3 of course because this works well in low dimensions. Yes, times the direction of the flow times u. And then you have so we call this one the singularity. The tangent space of the singularity in this case as I draw it is two stables and one unstable. So the idea here is that when you have periodic orbits that accumulate on these kind of singularities what's happening is that the direction of the flow at some point becomes almost tangent to the unstable manifold and it becomes almost tangent also when it gets in to the stable space of the singularity. So essentially what you're saying is that these two spaces get mixed because there are orbits that come in and out of here. So what you do is you propose let's get these two spaces together without some partial hyperbolicity. So we are going to ask this space to contract and this space to expand the area. As the definition I gave it is a hyperbolic structure and well, so this does fix the problem that I was talking about here with the periodic orbits accumulating on a singularity and having different kinds of splitting. But when you do this when you try to make this kind of partial hyperbolicity you are saying that the singularities have to be of one kind. So you have this kind of splitting and this kind of splitting and then you put these two together but if you had the reverse time of this singularity then you would have this splitting u times e u u So if you have periodic orbits that accumulate on this kind of singularity here you would have the space where the directions are mixed and then what you would have is that you don't really have any dominated splitting here which is worth looking at. So this works well in dimension 3 and dimension 4 and well, because there is it is not possible to make an example that has two singularities of different indexes like this accumulated by periodic orbits in a robust way. So since you cannot do that you don't have this kind of singularities related in the same class in a robust way in low dimensions in dimension 3 and in dimension 4 this kind of hyperbolicity which is called singular hyperbolicity characterizes in an open and then set the flows that have periodic orbits which are robustly hyperbolic that I will call star flows for the rest of the talk. But in higher dimension what you get is that this characterizes the star flows in an open and then set as long as you make the extra assumption that these two kinds of singularities cannot be in the same class at the same time or else well, you have a problem that you are putting on a priori because of the definition. Okay so there. So what I'm going to try to do now is I'm going to try to explain an example in dimension 3 of two singularities of different indexes that are in the same class in the same chain recurrent class. So I'm going to do that because so there is an example it is possible of two singularities of different indexes that are in the same chain recurrent class in a robust way but in higher dimensions so that is in five dimensions. And telling this example would be complicated and I don't want to get into that so what I'm going to do is I'm going to tell a baby example in dimension 3 which is going to be fragile but in which I can explain how you fix this problem when you have two singularities of different indexes and I want to explain something else by this. I want to explain that it's not so easy to make an example in which you say that a chain recurrent class has these things inside and nothing else. So when you try to build an example like this you have to take care about what happens with all the rest of the points because if you're saying something about a chain recurrent class you need to be sure that that is your chain recurrent class and that the other points don't go there later. So when you do an example in which you're saying something about the chain recurrent class you need to control what happens with all the points on the rest of the manifold. So I wanted to talk about this a little bit. So the idea is the following. I'm going to start with this drawing in a disc but I'm going to ask you to imagine that this drawing is in S2 I couldn't draw S2 in the slides but just imagine that I don't have the pointer either I guess. Let me see. Does this point? Yeah it points. So imagine that this this is a saddle singularity and this is the stable manifold imagine that it connects here by the other side the side that we are not seeing and this which is the strong stable manifold of this sink suppose that it goes to alpha 0 on the other side of S2 that you're not seeing so essentially you have alpha which is a sink no a source sigma 0 which is a sink but it's a particular sink it's a sink that has one strong stable and one weaker stable then you have F0 which is a source and then you have S0 which is a saddle Why do I do this also specifically because this way I'm controlling where the basins that I put are in this drawing I can control where all the orbits are going so what? Alpha 0 is a source so alpha 0 is a source 0 is a source this one is a sink and this one is a saddle ok so now what I'm going to do is I'm still drawing S2 as a disk ok so I'm putting S2 normally hyperbolic in S3 sphere and I'm adding a sink and a source so now I can remove a small open set around the the new sink I added which is this one and I can remove an open set around if you remember so I have this sorry I have this F0 there which is a source and I want to take a neighborhood out of that one so I took a neighborhood out of a source and then I took a neighborhood out of a sink so you can imagine this drawing as this one and the vector field goes in here and out here so now what I'm going to do is I'm going to grab another copy of this with the reverse time of the flow that I defined there and I'm going to paste the so this part with the corresponding part in the other copy and this part with the corresponding one in the other copy but not with the identity so I'm going to do a small rotation in order to paste them in a way that's convenient for me let's go back to this drawing no yeah this drawing so this drawing is the S2 which is in the middle so when you come here and you look at what's going on here in the blue part that I took out you can see that there are a lot of unstable manifolds of all the points in S2 that go to cut the disc that I took out so if you look at the intersection of these unstable manifolds with the disc that I took out you will have this kind of drawing so I'm grabbing all the unstable manifolds of the things that are there in the in the S2 sphere and then I cut them with the with the blue neighborhood that I took out and I get this kind of a drawing where this here depicts the basing of the of the source I took out of zero do you remember there was a source of zero I took it out and this here depicts that and this point here it's the unstable manifold of sigma zero cutting the the blue area I took out so this one is important because sigma zero has a strong a very strong stable manifold a weaker stable manifold now when I put it normally hyperbolic now it has an unstable manifold so this singularity if I choose the unstable correctly I can make it to be Lorentz like Lorentz like means that the unstable manifold has a stronger expansion than the stable manifold which is what helps me here to get like the expansion of area okay so that will make me one connection because I'm cutting the unstable manifold of this of this sigma zero that was Lorentz like with the stable manifold of the other sigma zero which I will call sigma one that comes from the reverse time which is exactly the same but with the reverse time and I can do this in a transversal way because I have to really do things badly in order not to get transversality there I have a lot of ways of pasting one this with the other and making these two things get transversal as in the drawing and I can make it also in a way that all the points that are here don't coincide with the points that are here because these points have the chance of being recurrent if they coincide but if they don't coincide they are going to sink their sources so this way I make sure that the only point that has any chance of being recurrent is the one in the unstable manifold of sigma zero and the stable manifold of sigma one now I need to make the other gluing and so I'm making this drawing here because so recall that this one is the one that I'm talking about now the one that is pink and the one that is pink when I took it out what I see in the boundary is well the intersection of the ah sorry there, the intersection of the stable manifold of sigma zero with that with the neighborhood I took out it's a curve because of the shape of the basin that I draw at the beginning of F zero so essentially what I need is that the two curves that correspond to taking this out I need them to cut transversally again that's very easy to do and in one side of the one side of the curve things are in the basin of a source and in the other side of the curves things are in the basin of a sink so essentially all I have to do is that these curves that have the chance of having recurrent points I need them just to cut transversally in two points and these curves are in the stable manifold of sigma zero and so they are in the unstable manifold of sigma one and so this way I get not only a cycle between sigma zero and sigma one which are Lorentz like but also I control that all that is not in the intersection of these two curves went to the basin of a sink and to the basin of a source and this is the way I control things for not getting other recurrent points besides the ones that I want okay so what is this that I have until now I will so I need these things I have this kind of singularity here I will erase the periodic orbit because we don't have periodic orbits as I said the only recurrent points are the singularities and the cycle between them so there are no periodic points then I have another singularity here wow that was awful and it's of the other kind so I will have unstable here strong unstable here and then stable here okay and I said that the stable of this one had two cuts with the unstable of this one so essentially what you have is something like this this is okay and then the other one had only one intersection so this goes here and the rest goes to sinks and sources so the drawing there is the drawing of the only orbits that survive and that are chain recurrent the rest is all going to sinks and sources so this is the drawing that I have and I have two singularities of different indexes okay so I managed to put two singularities of different indexes in one chain recurrent class but wasn't I doing this to say something about periodic orbits what which one which one why it's not transversal ah wait I didn't look so this goes here and this well the drawing is awful yeah no it's okay it's okay this is yeah there is only one that it's transversal the other one is not possible for it to be transversal and it will break it's a fragile example but when I was in university I was thinking about the normal space no it's not possible for it to be transversal if not it would be robust and it is not in dimension three it's not possible so you get this drawing and now you want to know something about the periodic orbits of the perturbations of this drawing it's kind of strange I mean I have no periodic orbits here so this is what I was trying so the main point I'm trying to make is that hyperbolic structures are nice because they allow you to say things about the neighborhood of a system only knowing one system so what I'm going to try to do in order to say whether or not the perturbations of this thing or the hyperbolic periodic orbits is I'm going to try to put a hyperbolic structure in it that's the idea but which one clearly not singular hyperbolicity because I made this example for it not being singular hyperbolic so what to do what to do so I mentioned another problem of flows I said that there are other situations that are different for flows than for defiomorphisms and that they involve the mixing of the direction of the flow with your invariant spaces and I said there was another way of solving this the other way of solving this when you are far from singularities is looking at the linear Poincaré flow so I'm going to try to look at the other kinds of solutions for flows and try to see if I can mix them together so what is the linear Poincaré flow the linear Poincaré flow is a way of forgetting about the direction of the flow what you're going to do is you're going to look at the normal space to the direction of the flow you're going to project the dynamic of the tension there and you're going to correct it when you flow it because when you flow the normal space to to a vector of your vector field it doesn't have to go normal especially if you're passing through singularities so it can get twisted a little bit but when you project back so the way I understand this happening better is with this sorry, I'm going to go back there later with this diagram that I did there which is okay in this case it's more general but maybe I will do the diagram there ignore the slide so you have the tangent space here you have a regular pointy machine here you have the derivative of the flow here you have your point that you flow it then you take the direction of the flow and you take quotient of everything that is parallel to it so you quotient here by the direction of the flow and you get the normal space to x and then here you do the same but with the direction of the flow you get this point so you get like this and you have here the normal space to this point okay, why I do this this way because this way I'm not depending on the metric that I have in the tangent space but usually people what they do is that they take the normal vectors to the direction of the flow then they flow it and then they project to the new normal space the metric of anything okay, so let's go back to where I was before okay so the linear point of flow is a way of solving the mixing of the direction of the vector filled with my splitting in the case I'm trying to find a dominate splitting but as I defined it here it's not defined on the singularity so I'm going to have to define it on the singularity I could for example add all the directions on the singularity because I just need directions to define a normal space so here I have the direction of the flow in every regular point I could have the direction of the flow and in the singularity I could put all the set of directions the projective space of the singularity but that will give me very little information because asking for something there to be to have some hyperbolic structure in that set it's not really going to make me have the results I want you're asking for too much and it's not really important in the end because there are some parts of the directions of the flow that are not playing any part in the chain recurrent class for example in this case the strong stable and the strong and stable of these two singularities they don't participate in the dynamic so why would you add them to your normal spaces where you want to consider your flow you don't, that's the point so things about this the first one the stable manifold tangent to the strong once it's outside of the neighborhood of the class the fact that this is outside of the neighborhood of the class is robust so I say ok this one is not playing in this drawing and it's not going to be playing in any other drawing that I could make of any of the perturbations of this system so it's out and the same for the unstable so in fact I only have to consider this plane here which is the center stable or center unstable and the same here in some sense this makes sense with the definition of singular hyperbolicity that we saw before so these two don't play and they won't play for the perturbations and these two will play for the perturbations when you perturb if the singularities don't get isolated if there are other recurrent orbits that appear they have only hopes of appearing almost tangent to the center spaces so we will call these the center spaces and these are the directions that we are going to add to to my set of directions to which I will consider the normal spaces so I consider the set of directions the projective space there and I consider here all the directions generated by the regular orbits and in the singularities I can find some stable space that is not playing and some center space that is or the contrary so these are the two singularities that are here there are not any singularities that are here and one has a stable space that doesn't play the other one has there is some mistake there this one should be unstable so this one should be unstable there but one has a stable space that doesn't play and the other one an unstable space that doesn't play I won't add these directions I will only add these ones and these ones so you have the projective space of this center space in one singularity and to that you add all the directions of the regular orbits that's your set in which you are going to take normal in that set you will consider the normal spaces to those directions okay and the good thing is that this varies apersemit continuously why do you want this to vary apersemit continuously because if not the hyperbolic structure you are working so hard to get won't tell you anything about the neighborhood of your vector field you need to have some good property of how this sets by perturbation if you hope to make a structure over them that varies well by perturbation so without base you don't get good structure and this is a good base okay so now we can define extended linear Poincaré flow in a similar way as we do here we take normal to every direction of the sets that we define and then the fact that there exists the linear flow here force you to have a linear flow in between the normal spaces okay so this gives me my candidate to find a good hyperbolic structure because this one the tangent space wasn't working and it wasn't working in a very severe way it wasn't a minor issue that I was having here with my with my tangent space because if you see for the tangent space here I will look at this orbit so I look at the tangent space of this orbit I get the tangent space of X here it's going to be if it's very near if I take it to be very near this singularity I can see a contracting space an expanding space and the direction of the flow is more expanding than the other direction so what you get here is ss times yes times X of X or something like this so this is more or less what you're seeing in the linear neighborhood and when you get to the other linear neighborhood you get like the opposite situation so XT of X when you are here XT of X you get the direction of the flow and then two unstable directions so this splitting you cannot make a splitting that is respecting this situation in the neighborhoods of the singularities and that is invariant because you are understanding the vectors that are in the on one side to the complete other side of the splitting from here to here so you get everything, every vector that's the opposite to a dominated splitting so you don't get a dominated splitting of the tangent space ok so you made a lot of this and you got another space in which you want to look whether or not you have a dominated splitting which is the normal space and the normal space it makes more sense let's look at the same orbit, this one ok this orbit in the normal space when you are in the linear neighborhood what you will see is the normal to X is going to be well some stable direction and some other stable direction ok so this one is stronger than this one and then when you flow it if you did it correctly you didn't but if you did it correctly what you should be seeing is an unstable and a strong unstable but that is not a problem for the dominated splitting because this one is dominated by this one and this one is dominated by this one so as long as you send these vectors to here and these vectors to here when you flow you get the invariant splitting and forgetting this is that the example we built before was having some care on whether or not the stable and unstable manifolds were intersecting transversely is to get this property that the vectors from here get sent to here and the vectors from here get sent to here ok so you can get the dominated splitting for this in this way but what about the stronger hyperbolic structures because I would like to say something about the periodic orbits when I perturb this if whether or not these periodic orbits are going to be hyperbolic or not and how do I do that so ok I said that the direction of the flow was bothering me but now I need it again and that kind of girl I guess so yeah the direction of the flow bothers me but not the information that the direction of the flow carries so let's come here if you had a periodic orbit that appeared here it's true now it has a you can make a dominated splitting that will extend and will be there when you perturb but you would want the periodic orbit to be hyperbolic and so when the periodic orbits are near the singularity of the periodic orbit around this point it's going to be very similar to the one around here which is seeing a contraction in the normal space a full contraction and here a full expansion so what are the hopes of me getting something hyperbolic for this periodic orbits well the point is I'm not going to try for the linear Poincaré flow to be hyperbolic I'm not going to try that because I know that there are things that have linear Poincaré flow which is not hyperbolic and that have all the periodic orbits robustly hyperbolic there is an example the Lorentz attractor for example so well there are many examples but as long as well yeah every time so my point is that's hopeless so I'm going to try to do something else somehow this I mentioned three so we can think about the singular hyperbolicity a little bit and remember that they were asking this to be area contracting or expanding in this case expanding in this case contracting so we need to recover this property somehow to our new flow that it's in the normal space and how do I recover this property the area expansion and contraction well what I need to do is to look at what happens in the direction of the flow compared to what happens in the normal space but in the normal space of the direction of the center because this one is not playing again so I don't need it so what I want is to translate the expansion of area of this center space to the normal and how do I do that well I grab a particular parallelogram which is this which is the direction of the flow and this which is the projection of the center space to the normal space of let's make another so here is the normal space here is the projection of the center space to the normal space and here is the direction of the flow so here is easy projected to the normal space and here is the direction of the flow OK, and I'm going to see the product of the norm of these vectors and see what happens, which is exactly as looking at the expansion of area. So I want this to be expanded because it's a way of translating the expansion of area. And I don't want anything, anything, anything with the other unstable manifolds. So what I'm going to do is I'm going to grab a function which has a support only on a neighborhood of the singularity, and that it's the support norm. It's going to be one outside of a neighborhood of a singularity, and it's going to be something interesting inside of the neighborhood of a singularity, which what it does, it multiplies my linear Poincaré flow with the direction of the flow. But it doesn't do it in all the linear Poincaré flow, but only in this center space. So it's going to be like this. This is the linear Poincaré flow. OK, and so this one, I can, suppose XB, I can write it in coordinates of the dominant splitting. So you can think that this one is at ESS, XB, and this one is at the center space. Well, this changes when I move from one place to the other. So I will call E and F. And I can write the linear Poincaré flow in coordinates of the dominant splitting. Well, I do that, and then I multiply, for example, when I'm near to this singularity, I grab a function H, and I want this function H to be. H is going to be the expansion along the direction of the flow. So it's XT of X, X of X. I want H to be this inside of the neighborhood of the singularity, and I want it to be one outside. OK, so I have that, and I multiply this not everywhere, but just on the space which needs to recover the expansion of area, which is this one, and here it corresponds to this one. OK, so then I get this one, and let's put some gnocchi like this, which is here it's the same, because this one wasn't playing on that singularity, and here is this one times H. I can define another H, let's call it G, because calling this thing the same is a problem. G here, that does exactly the same, but only in this neighborhood. It's like H, it does the same thing of H, only that here it's one, and here it's the expansion along the direction of the orbits. So I can come here and multiply G here, so this one recovers the idea of expansion of area in the center and stable space and a contraction of area in the center stable space, this one. And the whole thing is that this one, if this one is hyperbolic, then all the perturbations of these have all the periodic orbits hyperbolic. OK, that's cool, I can now detect whether or not this is a star flow or not, but even more. This can be done in higher dimensions, the idea is the same, you only multiply the expansion of area in the spaces where the directions are mixed, and you can make this in general in higher dimension. And so, first of all, I forgot to say, this that I made here is not any function with no sense at all, this is a co-cycle over the projective space, and it varies well. So if this is hyperbolic for one vector field, then it's an open property for the vector fields. This is important because if not, it's not a hyperbolic structure, it's not what I'm looking for. And so I made this definition and I took all this care with all of these because this kind of definition helps fix the problem of the dimension of the singularities, and now you can recover all the proofs that were done in the cases where the singularities were of the same index, because you just recover the same proofs, it's not like you're doing anything else, you're just putting the new definition, grabbing the machinery that was already there, and making things work, and so they work. With this definition, you get in an open and dense set of star flows, a characterization via a hyperbolic structure of them. Okay, so not only that, what I'm trying to say is that this kind of way of understanding what happens around the singularity, so looking at this kind of co-cycle, and looking at the, now not only hyperbolicity, but any hyperbolic structure, looking at it instead of in the tangent space in this, in the normal space with this co-cycle, you can now translate the way you were making the definition of hyperbolic structure to this setting, and when you do, you can define singular volume partial hyperbolicity in this kind of way, and you recover the other results of defiomorphism, the other one I talked about today, which is, okay, if you have something that is robustly transitive, then it's volume partial hyperbolic, or if you want a robustly chain transitive, then you get in an open and dense set. And so, still there are a lot of things to do and to understand better, a lot of them I just put some of them, but, well, this is not singular hyperbolic, as I said, but it has this other kind of hyperbolicity that I talked about. So there are things that have this new kind of hyperbolicity and that are not singular hyperbolic, even in dimension three. In dimension three I said that singular hyperbolicity characterizes open and densely the star flows, but there are things in the complement of these open and dense that are hyperbolic for this kind of definition and not for singular hyperbolic, so another question would be, is it necessary to use open and dense in dimension three? Also, the proofs are highly dependable, they depend highly on the fact that the periodic orbits have all the same index, and this in dimension three you more or less have it for free, so maybe you could say in dimension three that all the star flows have this kind of hyperbolicity, maybe, but I don't know. Another thing is that, okay, you can say that the star flows have this kind of hyperbolicity, you can detect a star flow only by looking at this co-cycle, fine, but can I say something about the number of chain classes a star flow has? If it was a stardifio, I can say a lot, I can say the classes are finite, I can say everything that happens inside the class, I can say they are omega stable, I can say everything, but in flows, when you have singularities, they are not omega stable, these star flows, okay, but what can I say about the dynamics? Other than the periodic orbits are hyperbolic, can I say something about the amount of chain recurrent classes? And here I only know partial things, so not the full answer I would like to have. A question related to that, the star property talks about periodic orbits, so do I always have periodic orbits in something that is a star flow? Evidently not, but are these kind of things always fragile? If I perturb something that is so-called a star flow, do I always get a periodic orbit in the class? I have no idea, and this is the main problem with the question just above, so that. That is all. Can you give us a question about robust transitivity? Do you have examples beyond the one we know for the pharmacisms or other factors? So examples that are not star flows, but that are robustly transitive, maybe combining singularities with different indices, do you play with that? No, I didn't, but I'm sure there are, but robustly transitive things. So I stated it with. Do you have an example about robust transitivity, so what are the examples? In fact, I'm always thinking about robust chain transitivity. So this is a problem for me. I never think about anything else. And well, it's just there is these conditions you are doing all the time for getting the expansion. Maybe if you don't ask, for example, the expansion of area there, you still get something that seems to, I don't know anyone, any example now, but there must be. So there is this example by Christian, and I don't remember the precise citation, but it's Christian with other people, with some Chinese guys that I don't remember the names of, which is an example of something that is robustly chain transitivity that has periodic orbits of different indexes. So it wouldn't be singular hyperbolic or it wouldn't be any of that. It has singularities of different indexes, and that one with this is going to be, but I don't know the precise, the names of the other guys, sorry. Leaning. Yeah, that. That, yeah, and there are surely others, but I don't know. What? There is no splitting on the creation of three, the full-dentioned space. No. There is a splitting of three point A to five. Yeah. For negative and negative. Could happen, I have imagined, that there's no splitting at all. At all? What do you mean? The full-dentioned space, you have the dimension five, or is that right? There's no splitting, but it would have a star flow and some kind of a mid-splitting on the way. Yeah, so the example, we will. The tangent, or the non-linear? I guess of the tangent. So I'm not completely sure, but I think the example on the dimension five can be done to not respect any splitting. What?


Okay, everybody. This is it. This is the big closing keynote. I put on my white jacket to commemorate the event This is Will Reynolds. You know Will Reynolds. You may know him from real company shit You may know him from his work at Power BI The Seer Agency one of the best companies you know on the East Coast and the West Coast too making differences Not only in the SEO and PPC world but in their community just an awesome all-around great company and a great guy He's also one of the most honest people in the industry, and that's why we always enjoy him. Let's welcome Will Reynolds Howdy folks Will Reynolds here from Seer Interactive and as you know, I like to study disruption within marketing and This time I'm starting with the CMO and realizing some of the pressures that they're under What their goals and objectives are and ultimately how can we use the data that we already have at our fingertips to solve the CMOs of the future's biggest problems Because I've been looking for a while at what drives success for CMOs versus failure And I don't have time to get into all the failures today But when I look at the studies done around CMOs of the top 2,500 companies in the United States They're seeing that things like customer data and analytics, but not just having customer data and analytics It's knowing how to use that data to make better decisions Then we see here the enterprise-wide business mindset And we also see voice of the customer at the leadership table with voice of the customer being their number one goal and I think that we as search professionals content marketers and marketers that deal with search I think we've got a really good chance to own the customer journey Because I think that we get more information about the customer journey than pretty much anybody else does I just don't think that we're using that data that we're already getting all that efficiently So let's start with the story once upon a time. There was a CEO and the CEO said this Do you all know that? 2020 marks the 130 year anniversary of this quote a 130 years ago this was a problem That CEOs had about marketing and you know what? When we think about our role and understanding the customer and the customer journey I will tell you that part of what leads to that inefficiency in Spend on marketing is the fact that we're spraying broader than we need to to target our customers And I will tell you the less you understand your customer the more you were going to have to spend to acquire that customer But it's all good now, right 130 years ago. They didn't have Google Analytics I'll tell you Having Google Analytics is a lot like having data It's not necessarily knowing what to do with it Why because I do a lot of analysis on inefficiency and marketing spends and I will tell you that while it may not be 50% 130 years later with all these cool tools it wouldn't surprise me if it wasn't 30 and that's not a lot of progress See because so often when we say well, we've got analytics. I'm like, yeah, but analytics is a lot like being punched in the face Don't you wish you know that guy was going to throw that punch 30 seconds earlier? Analytics is so often a tool that you know, you check it once a week or you look for certain things And by that time you finally look at it You realize I would been getting punched in the face for the last three weeks and my analytics is just now telling me that it's a problem in This current environment more than ever I would say every dollar is under an extreme amount of scrutiny right now Which means CMOs are being asked tougher and tougher questions than ever and those questions roll down to us So what are we going to do to help CMOs in this current state of affairs? But actually this has nothing to do with coven Things are already looking pretty bad for the CMO when it looks when we look at the C-suite There are articles around why CMOs are always the first ones to be fired when business objectives aren't hit Large companies are leading the charge to completely get rid of the CMO role And they're oftentimes replacing it with a chief growth officer or someone else But they're getting rid of the role. They're re-evaluating the role And some of these companies are starting to say whoops. We made a mistake, but still the CEOs were thinking I don't know if I need that CMO anymore And you can see Gap hires a CMO gone in 11 months. They redefine the role lift eight months Gone we shaped up the marketing department It's like man We constantly have these arrows in our backs as marketers And if the people who write the checks to us to do marketing for their organizations are these folks Then how can we help them look more like those successful CMOs that we've seen? Because every single study that I've looked at shows the data that the CMOs have the shortest tenure in the C-suite Who all right So there's a little bit of a power play here Let's just break it down in the role of the CMO if data is how successful CMOs operate Well, CIOs are the one that own that data for them to get CFOs are the ones who approve their budgets and CIOs are the ones who hire them and choose who to pay how much to pay them So the CMO Wow in the C-suite is really at the mercy of so many other people to be successful in the role and so often If they don't all work together we get the blame and we're the ones who are fired first So I have the ear of some CMOs and you know, you kind of think way great I've got the ear of the CMO, but there's a there's a new sheriff in town and Remember what I just said the CMO is always at the whims of the CEO CIO and CFO because they own the strings to help marketers to do their jobs and This guy has a chance to disrupt that even further Because he's got the ear of the CEO the CIO and the CFO and remember They got the puppet strings often times in many organizations over the CMO and He is really good at translating and building Solutions that help us to take marketing speak into the language of the CEO CIO and CFO Now think about your job How easy is it for somebody to connect your work into the language of a CEO a CIO or a CFO? And if you're not doing that then you're not setting up your CMO or your marketing leadership to easily translate your work Into the way that they look at the business. I Will tell you that that person is Brian Whipple CEO of Accenture Interactive Whom we are now starting to compete with on SEO So when the first time I heard a client say hey, you know We're looking at Accenture to do our Accenture Interactive to do our SEO and I have so much respect for Brian So much So I googled it I googled Accenture Interactive SEO and I look at the first result and it's a Philippine site and I'm like man their hreflang is off And then the second result is an old piece of content and the third result was a PDF. I Mean, okay, then I looked at Deloitte who's also starting to offer SEO Services and coming into our space and I'm like their multi-site ranks number one two and then Glassdoor They don't even have regular content. That's that's ranking appropriately to talk about their service offering Now I think a lot of us who do search in the room We're kind of laughing at these guys a little bit, right? Like they're gonna do SEO. They can't even get their hreflang, right? Well, let me remind you I've never seen the word hreflang in a quarterly report from a CFO or CEO Do not think that these guys are not going to come and be in our boardrooms having conversations right next to us Why? Because they've done it before the Omnicoms the public's is the IPGs and densers of the world really kind of fought against these guys Sorry for the pixelated slide. I couldn't get this one on correct But then in a matter of just a few years they went from they don't do what we do to oh my god, they're taking my customers These guys know how to move fast because they have the ears of the CEOs CIOs and CFOs and organizations So now I need to understand how does Brian Whipple talk? Listen to the things that he's saying Look at this quote and think that is what is making CEOs who are over marketing CIOs who are often needed for marketers to be more data-driven and CFOs who approve the budgets This is what he's saying to them and getting their buy-in over our points of contact. Okay? Now you might be thinking well well consultancies you're worried about that because that's your competitive world But it's like no no no no no no no no if you're in house Somewhere you have a CEO a CFO a CIO and a CMO and these dynamics are happening there, too So how do you set up your in-house? Chief marketing officer chief growth officer to be speaking the language of the CEO and CFO and CIO Because the result if we continue to take our information and not pivot it and turn it into a way that works for those folks in the C-suite Well, we saw what happened already The Accenture's Deloitte's cognizance and IBM's did acquisitions came into the space and are now making the people who owned marketing for Sometimes 50 60 80 hundreds of years. They're making them sweat and they're taking their business You know next time somebody starts talking about buzzword bingo about your CEO CFO or CIO Tell them to shut up Because if this is the language they're speaking and we want to change their minds Then maybe we should also be speaking their language as well We do not want to be the translator who only speaks one language If the language you speak is only SEO and it's not the same language as the CFO Then you're gonna make it harder to get SEO work done because I'll tell you this I don't know a whole lot of CEOs who read search engine land But they're the ones who write our checks Zilz zero none of them. They don't read it. Sorry Which is why on our site? We've got a couple of resources where we talk about how to use the reports where the CFO and CEOs talk to Wall Street because that's how they keep their jobs and how we can translate our digital marketing efforts Whether it's this post or this one on how to use financial statements to help you do SEO We're sharing that information with you because we think it's so critical for us to be a part of helping people to speak the language of the C-suite so we can get the respect that we deserve at the table and Remember sometimes SEO divisions and I wrote about this in a blog post are better run by people who are in SEO So here's Crystal Larry and me talked off on the right And here's our SEO revenue over some time period and you can see what happened to the company We started flattening out as me an SEO guy was running the SEO division The people who come in with their backgrounds in with their MBAs and their understanding of business Took our SEO division to levels that I never could on my own as a day-to-day practitioner Because I still needed a little bit of practice on speaking the language of the C-suite and it was natural for them Here's one SEO guy. I just respect the hell out of Stephen Bajaya and he said this And that's hard That's hard to read guys like the worst thing But I think he's right, but I'm gonna show you in this presentation how to overcome that issue So let's start the process of saying, okay, well you set it up. I get it. There's different language out there How do we do that? What does that look like and feel like? Well first thing I want to do is remind you of the amount of clues that we have every day at our disposal to better Understand customers. I search for the word transmission Take a look I could say oh you rang for the map pack and be done my job Oh, you rank in organic and be done my job or oh a snippet shows up But there's a lot more information here There's not just that a map shows up But it's the position that the map shows up if a map is in the first position Then Google feels really confident that this is a local base search if it's in the 10th position They feel less confident that data points important Then I want to be able to understand the distance from where I searched to all those locations So I can understand where does my client need to locate their new their new offices or their new? Stores if people showing up and searching on Google is important to them Then I need to be able to calculate from a zip code To these locations to see what's possible and then there's reviews there and there's words in those reviews Which will give you clues to what people think about these different organizations and then below that we've got the people also ask questions And think about all the data sitting in the people also ask You've got the question itself You've got the answer You've got a date in this one which tells you freshness of content You've got the domain which is car brain and you've got the URL This helps you to get look at all those clues sitting there to potentially be harvested to better understand the voice of the customer You search for the word transmission Below the map and below the people also ask you've got software information sites definitions dictionary.com Wikipedia you've got a piece of content in here that's related to COVID I bet you you weren't thinking COVID when I said the word transmission and then there's stores and retail below and yeah COVID because for a while the CDC was at the top of the second page or the bottom of the first page Thank You Amy for that one For the word transmission So let's think about something else that's going on here in order for us to understand the voice of the customer That means that we need to also be consistently monitoring How these things are changing over time because we live in such a fluid environment And my belief is whether it's a thousand keywords or a million keywords whoops Whether it's a thousand keywords or a million keywords. It doesn't matter We can no longer track a hundred or 200 or 300 keywords and think we've done our jobs We need to evaluate all those different clues at scale because we are not clueless If you were to look at any other Marketing channel out there. I honestly believe that if you can harvest all those clues We're actually clue full But we don't always have the tools to take those clues and turn them into better customer experiences And if you're thinking customer experience, ah Remember the people selling the CEO CIOs and CFOs and the successful CMOs are all talking about customer experiences these days and We need to make sure that we're constantly challenging ourselves to say how am I connecting this work that I'm doing right now to customer experience For instance when I just showed that a multi-site ranks for Deloitte The goal isn't to say that's wrong for hreflang. It's to talk about the customer experience Are they getting the wrong language? Will they not be able to complete their tasks? Will you not be able to analyze the impact of the work that you're doing yada yada yada? We have to get our data out of these inefficient silos But let's talk about the coronavirus a bit Coronavirus comes and the world changed for almost every marketer out there We had CMOs who were like oh my god My new reality is my CFO for the US region just said I have to cut my budget by 24% next week And there's panic because then my CMOs go in I got two days to figure out what I'm going to do Panic So what we did is we worked with one of our clients and we started brainstorming and saying okay What can we do to help you here with the data that we have and we said okay if you're already paying for clicks and paid and You are ranking in SEO in the top three positions You might be able to get some of that traffic for free But if you're not in the top positions you might need to keep paying to get those conversions because you have no way of capturing that user So let me give you a little bit of a peek into the system that we built because I didn't want to build that system For one client and show my team how each person now needs to downloads and CSVs and then open up sheets And then transform the data and then you know use this plug-in that plug-in I didn't want my team member spending time doing that. I wanted them to open the file and get the answer So we engineered the data in BigQuery to say bring in every search term We've been doing this now for years to bring in every search term out of PPC every day We then run the ranking analysis on that every day so we can get the rank and we're doing this for every client So what that means is here's the file. It's live Where I just said show me the rank between one and three where my clients got at least one conversion and Over to the left-hand side here You can see that twenty point five six percent of every dime that every client who trusts us to spend money on their behalf On paid is spent on keywords that fit that criteria and then on the left side where you see I have a client name I had each individual client and what percentage of their spend or on keywords where they rank between one and three So you can see that top client has a 59% of all their search of all their search spend on paid We're on keywords where they already rank in the top three So if their CFO comes in and says you got to get me that answer in two days, and I need you to cut 24% They know they're safe that same CFO if you're the client at the bottom at thirteen point two six percent We got to go find in another eleven percent for you And this is what it sounds like Hey client you spent this much on these many words that have converted Where you organically rank in the top three and that represents X of your budget And if that number X is over what you just been asked to cut we're done right our work here is done Or we found other things for clients where we said hey Let's run an analysis across every client where we say where they spent money on a keyword that's gotten over 20 clicks So it's got enough action now that if it's not converting yet. Maybe it's not going to ever convert Where they already do rank in the top 10 so they still have some visibility and then the ability to say hey That's this percentage of your budget helped our clients to know instantly where they might need to where they might be able to make cuts without hurting their overall business and We did that for every client in two days because we had built a highly efficient data flywheel that enabled us to hypothesize and jump instantly into action and We wrote a blog post about it and our system is so efficient right now that if anybody watching this today said well I want that literally from the time you give us the access in 48 hours We could turn around and have that done for you because the system is so efficient I mean it would literally run minutes and this might take us a couple of days to do the analysis and get it back to you So when my clients are thinking oh man will when that second wave comes I'm if I get asked to make cuts It's like whoa when that second wave comes all I got to do is we've already done the hard work So we've already built the infrastructure underneath. So all I've got to do is hit refresh on the file that I already have built One click will update for every client every data point you saw to help us help them through that tough time of how they make cuts Because see as you start to go and understand your customer and Understand their experience when you find one-off things I get impatient when I find one-off smarts in my organization and I go how can I scale this? So every single client can find this kind of thing if it exists in their data with one click on a refresh button Let me give you an example So we were doing an analysis of the words that people were using Pre-imposed COVID and looking at the impressions impression growth over time and one of the things that we found Covid hits people were very very very very worried about the FDIC We haven't seen a spike like this since the 2008 financial crisis. So what this tells me is for a period of time There was a significant amount of people who were worried about the safety of their money for the FDIC So if you're a bank and you're going after Banking keywords maybe for that two-week stretch or so it would have been better to communicate to people or add into your Communication around how safe you are not necessarily how high your rates are because there's a good chunk of the audience And a good chunk of your customers at the time might have been worried more about the safety of their money in that return And what we had here is An analysis that we are now running currently for every client Well, we're able to say look at the different engrams the different word pieces and I can see for instance That anatomy is getting a lot more impressions, but we're not converting those people as well That's a different strategy. So I want to be able to say to our clients instantly Hey, this word people are searching for or people are searching for that word more And what does that tell us about how we might need to tweak the customer experience to better match these new concerns That are showing up more and more We did this for one client and I already had the highly efficient system and the right team and God knows I got a great team who were able to spring into action and within a matter of weeks built this out so that we Could do this for every client That's what it feels like when you've got a data fly We'll let the ready that cuts through all these words and helps you to better understand your customers See we're already getting these clues guys. They just exist in these silos It's our job to take the data that everybody else has just like you and I you got paid data You got scraped data from from rankings. I got the same thing But we're transforming it and making it accessible and translating it into value for our folks in the C-suite Because every time you get a ranking for a word like SEO in your rank software, guess what? You're also getting all the other clues as well And the question is are you ignoring these clues? If you look at the word SEO company, it makes sense to bid on that word Yes, it does. I'm an SEO company. I should bid on the word SEO company But there's a big clue in organic in the first spot that tells you that people want local So if you are a company in Utah and you're bidding on the word SEO company Google's learning has already taught us that people want local more than likely So you might want to change your bid strategy based on what Google's already learned about the customer Which is the average person searching for SEO company once a local solution? Google's already learned it. We just have to transform our marketing to take advantage of it And you see this concept of just getting more data in And saying that oh the more data I get I can make better decisions is not true There's a massive roadblock between these things and it's interpreting that data to turn it into actual better decisions We get enough data, don't we with all these freaking tools that we have at our availability We need to find a way to make these things all work better together But keep in mind this isn't just about getting me more data It's about transforming and translating that exact same data into value for the C-suite Because remember the other thing that successful CMOs the CMOs were holding on to their jobs longer than their cohort They're strong at being the voice of the customer at the leadership table because you know what a CIO doesn't know what the customer wants all the time a CFO that's not really their thing So we need to double down on helping the successful CMOs and chief growth officers at our companies be a stronger and stronger Advocate for the customer by tearing through our data and saying hey, there's clues that Google's learned How can I use those clues to better understand what our customers are seeking? So let's talk about a few customer journeys Let's take the word joint now. I want you to stop and think about the word joint Come up with what you think that word could mean and now let's go through a journey together. I Was staying at this low-class joint the bed was hard as a rock. So now my joints hurt I had softer beds when I was locked up in the joint My day got even worse when my wife served me papers for joint custody. I Would just love a good joint recipe because man. I need a good meal right now and a joint to relax Now look at all the different meanings of the word joint And I think this one example will give you a feel for how the word joint can have a lot of different meanings And who knows the meanings of those words in context better than anyone else on the planet? Google does So when I add the word joint and from a checking account Google knows exactly what the right answer is now. I want you all you smart marketers out there to stop and think Okay, I'm at a bank and I'm doing marketing for our checking account and Somebody says well, what's the best result for joint checking account? Think about what you would the page you would build to talk to that customer and give them the best experience possible And now I'm going to click on city bank citizens bank and Fulton bank Ready, let's go show these old school marketers who don't have data flywheels. They got gears, but they're all crusty and rusty Here's city bank Now I want you to go back to what you were just thinking about Joint checking accounts and how to market a joint checking account now. Look at the text. Look at the fact. There's only singular person here Citizens back they actually have a page that ranks number five organically for the word joint bank accounts But they're showing this page and they're paid because they have siloed crusty rusty Gears this page doesn't say anything about joint checking accounts And they've already done the hard work to build a page that earned the ranking organically And here's the page. We're driving people to Customer experience wise. I think we're a bit off folks. Don't you think so and then let's look at Fulton Bank And none of these banks mentioned the word joint on the page They didn't mention the word join at all They're not speaking their customers language When is it a good marketing idea to not speak the language of your customer? And these are the kind of thing that CMOs are under pressure on because a CEO Randomly searches for this finds it and goes how is it that we're not doing this a CIO goes how are you not using all that data? I've been giving you to fix this problem and how big of a problem is it and how often is this happening? And CMOs gonna go I have no idea. They're gonna talk to them Hopefully they're not hopefully gonna not talk to them about match types, but they're gonna ask somebody just like us Why this has happened and what's gonna be our answer?  It makes no sense Why would you spend money to send somebody to a page that has no chance of actually solving their problem or speaking their language? But one marketer my friends seems to have some pretty efficient gearing going on and it's simple Look at this page. Is this the kind of page? You thought you might build for the word joint checking account because it's the kind of page I would have built it shows two people Because we know what we mean when we say joint checking account It uses words like share and yours mine and ours and the next image is also of a couple They talk about together and shared and look how often they use the word together together means the two of you together And then there's a picture of two lovely people on the beach On vacation together Hmm, who do you think is proving that they best understand the customer and that they've got an ability To understand that the word joint in front of checking account makes the word mean something different And they're able to execute and react to it Who do you think has the strongest flywheel? If you were a marketer and you said okay, I can hire a marketer from any of those companies or their their agencies Who would you pick? Who seems to have figured something out that everybody else hasn't and that my friends is what I consistently show you on this stage at Moscon for the last few years All right, so now let's think of another customer journey. I Recently got this ad on Instagram Instagram is a mobile platform Yes, right. We all know Instagram is a mobile platform. So I'm looking at this ad and I'm going holy smokes I've never been to their website before and these are my actual shoes They are really good at targeting me on social And I bet you somewhere the team who's behind showing ads to me that are the exact shoes that I have They're like, oh, yeah If you're at Facebook or you're the targeting vendor or you're the social person or the social team at Nordstrom You're like our stuff is so good That we can target people with the shoes. They're currently wearing high freaking five Not so quick Because this is a very efficient gear on social but everything else around them is old crusty and rusty The page wasn't even mobile friendly.  Like what is that like how? How did this happen? I wanted those shoes and now if you showed me those shoes and I love those shoes and you make the Experience hard and you don't have my size you just paid for me to go find that product somewhere else for somebody Who didn't have to pay so now I'm going to Zappos. Thank you Nordstrom for paying for Zappos's conversions This is where we need to adopt an enterprise-wide business mindset How do we get the data across the enterprise bring it together and make all these all these gears come together and work together? Because if you break down this problem, there's a way this could be solved at scale You take every Instagram ad and you get all the URLs that you're driving people to that data exists You run those URLs through a tool or an API that can check to see if it's mobile friendly and you do this at scale every day And then you say I'm going to take the images in my ads and run an image lookup via an API to my product database So I can make sure that I can then pull the inventory for that product So now you've got an efficient flywheel that says I'm checking to make sure my pages are mobile friendly I'm looking at the at the the product that I'm targeting that person in that ad I'm then looking that product up against my own inventory to see if I actually have a high enough stock to keep Advertising or maybe I could shut it off That my friends is how we get out of 50% of my advertising is wasted. You build the efficient systems to protect those budgets And that's why we can't just rely purely on this using the same tools You know many of us out there have a client in a space where we compete with each other And I'm always thinking where can I take data from tools that we all have and pivot them Turn them in a new way and get us and our clients that information faster so their flywheels going faster than ever You don't have this it's gonna be hard to compete with somebody built a system to find the things that you can only check once a month Or once a quarter Let me give you another customer journey before I wrap up Let's take the word enterprise customer support And I want to show you the journey. It's not so much a customer journey It's a journey through siloed data sets and how we can be better And this is what I've been talking about on stage forever So if I take this word enterprise customer support and I take it to my SEO team If they got to make a decision on whether or not to go after that word They're gonna look at monthly search volume and they're gonna go and that volume is low skip it 50 searchers a month skip it But if I can combine my SEO gear and my PPC gear in an efficient way I Will now be able to say wait a second my PPC data is saying Excuse me my PPC data is saying That word drive some conversions So while the volume is low it seems to drive us some people who pay our checks at this company Maybe just maybe we should target it because now I've got new data Which are is that word converting or not in paid? But we're not done yet There's analytics and what you and I know about analytics is very often analytics will have multiple other goals in there So let's just say now. I'm taking my MSD from SEO whether or not that keyword converts from PPC And I'm also saying wait does that keyword Land people on a page that is highly likely to lead them to Subscribing for emails or signing up for webinars which I might see is highly valuable as well Because maybe I've got a great way of getting people from webinars and email into becoming customers So now you can see that the siloed SEO was like nope SEO PPC together was like Maybe SEO PPC analytics data together goes This is looking even stronger, but this is not the holy grail my friends The holy grail that I'm working towards because I already have my SEO PPC and analytics data connected this way The holy grail is for me to get buy in for my clients To give us their CRM data not their customer data But I want to be able to push data into their CRM. So in this instance, you could say wait a second Enterprise customer support. Yes monthly search volume was low, but it did convert a good bit So we had a couple conversions this year on that word and then my analytics goes wait a second I'm adding data in to to that word to let you know that that word in the page that those people land on it does a good Job of driving us email subscribers, but the holy grail my friends is the CRM Could you imagine if you could say wait a second SEO? We're going after this word because I now know that we've got three deals that have closed in my CRM On this keyword as a result of targeting it and paid So if I know that those are highly valuable customers Why would I not want to go after this word and imagine if you took every word and ran it through these four things? every day with just a refresh Imagine the decisions you could make and how much quickly how much more quickly you could find opportunity to help your clients your Bosses etc. Take advantage of these opportunities before anybody else is even thinking about it And that my friends is the power of the flywheel So just maybe maybe the best thing to happen to search data is that it did end up in our hands Maybe we just didn't know what to do with it And maybe I've been showing you on this stage of mods company the last three or four years now How to actually it's probably in six years that I've been talking about listening to customers using data Maybe this is the year that you decide to do it. I'm going to leave you with a story about the difference between an architect and a builder I'm currently working with an architect and what he says to me as he goes will Life's not all about vacations What makes you fight? Everybody gets along on vacation, but that's only seven days a year 14 days a year all the other days of the year You're at home with your significant other And he says to me what makes you fight? We're not looking at houses yet or examples or flooring He says what makes you and your wife fight what gets on your nerves about each other And you know, I tell him a couple things that are going to stay between me and my wife because you don't need to know And then he says what makes you smile and I go Oh man It's seeing my sister pushing my kids on a seesaw or hanging out and watching my kids just play together and grow together And it's just so meaningful to me to just be able sometimes to catch that little peek of them being kind to each other for a couple seconds This is what he talked to me about he didn't talk to me about the flooring Which is our version of the keyword or the href lang he talked about my dreams and what makes me smile And he said I'm gonna eventually build you a house that minimizes the things that upset you about the relationship with your wife and maximizes your smiles He said I'm gonna build you a house with a courtyard.   I come to the site. I lay bricks for some tech dude that does conferences That was how they see their job The problem with not seeing the bigger picture of where you fit in the larger ecosystem around the customer experience and dream is this If you wake up every day to lay bricks and you're 50 You'll be all right If you're 25 This machine's coming for you And then what are you going to do? That's why it's so important for you to connect to the why of the customer and use that same search data to connect to their why I think this is my eighth or ninth straight moscow And I just want to remind all of you that there's an architect inside of each of you But many of you have that architect hiding behind a bricklayer mentality You have all the tools at your disposal You get ranking results. You can look at all the titles and descriptions of things that are ranking You can see the transmission just changed you get that paid data join it to your seo data, which I showed you all how to do three years ago You have the tools to be architects I just can't wait to see all of you take advantage of those tools. Thank you so much for your time I'm will reynolds. Hang in there and hopefully i'll see you next year. Have a great rest of your moscow Take care


So, here's your question back for why this course. Number one, which course are you going for? Number two, is it a master's or a bachelor's? Number three, what's your specialization? Number four, which subjects are you taking? Number five, how will this course help you in the future? Number six, why this course? Number seven, how many courses are you taking per semester? Number eight, what are the names of your first semester subjects? Number nine, what is the difference between X and Y? Number 10, which subjects excites you the most? Number 11, how many semesters do you have in this course? Number 12, do you know of any capstone project that you will be doing in the course? So, these 12 questions were essentially all the questions asked about why this course category. So, make sure that you go through this checklist and prepare yourself.