TOPOLOGICAL ENTROPY AND PERIODS OF SELF MAPS ON COMPACT MANIFOLDS

Let (M, f) be a discrete dynamical system induced by a self-map f defined on a smooth compact connected n dimensional manifold M. We provide sufficient conditions in terms of the Lefschetz zeta function in order that: (1) f has positive topological entropy when f is C-infinity, and (2) f has infinitely many periodic points when f is C-1 and f(M) subset of Int(M). Moreover, for the particular manifolds S-n, S-n x S-m CPn and HPn we improve the previous sufficient conditions.