On topological entropy, Lefschetz numbers and Lefschetz zeta functions

In the present article we give sufficient conditions for C-infinity self-maps on some connected compact manifolds in order to have positive entropy. The conditions are given in terms of the Lefschetz numbers of the iterates of the map and/or its Lefschetz zeta function. We consider the cases where the manifold is a compact orientable and non-orientable surface, the n-dimensional torus, the product of n spheres of dimension E and the product of spheres of different dimensions. (C) 2019 Elsevier B.V. All rights reserved.