Abstract
The topological complexity of the intersection of a submanifold, moved by a dynamical system, with a given submanifold of the phase space, can increase with time. It is proved that the Morse and Betti numbers of the transversal intersections “generically” grow at most exponentially, while for some special infinitely smooth systems the topological complexity of the intersections can become larger than any given function of time (for a growing sequence of integer time moments).
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