His proof relies on the existence of 'transition chains' of 'whiskered' tori, that is, sequences of tori with transitive dynamics such that the unstable manifold (whisker) of one of these tori intersects transversally the stable manifold (whisker) of the next one. Arnold conjectured that "the mechanism of 'transition chains' which guarantees that nonstability in our example is also applicable to the general case (for example, to the problem of three bodies)."