Popularizers of topology often describe this shape as equivalent to a coffee cup.
If the rotation numbers that define an allowed segment of phase space with this shape are sufficiently far from being rational, then that shape will not be destroyed under perturbations. That consequence of the KolmogorovÂ–ArnoldÂ–Moser theorem applies to "invariant" ones of these shapes that are defined by actionÂ­angle coordinates. BornÂ–von KÃ¡rmÃ¡n boundary conditions can be visualized as placing a system on the (*) surface of one of these shapes. Confined magnetic fields can be described by poloidal coordinates andcoordinates named for this shape. The dzÂ­squared electron orbital has one component with a dumbbell shape and one with this shape, which is also the shape of a tokamak chamber. Popularizers of topology often describe this shape as equivalent to a coffee cup. For 10 points, name this mathematical shape that resembles a donut.
If the rotation numbers that define an allowed segment of phase space with this shape are sufficiently far from being rational, then that shape will not be destroyed under perturbations.
torus