Todd Fisher (Maryland)

Superexponential growth of the number of periodic orbits for non-hyperbolic homoclinic classes.

Abstract. We show there is a residual subset $S(M)$ of diffeomorphisms of $M$ such that, for every diffeomorphism in $S(M)$,   any homoclinic class containing periodic saddles of different indices has superexponential growth of the number of periodic points inside the homoclinic class. This is joint work with Christian Bonatti and Lorenzo Diaz.