© 2017 University of Houston. 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 C1, and (2) f has infinitely many periodic points when f is C1 and f(M) Int(M). Moreover, for the particular manifolds Sn, Sn× Sm, CPn and HPn we improve the previous sufficient conditions.
|Journal||Houston Journal of Mathematics|
|Publication status||Published - 1 Jan 2017|
- Compact manifold
- Discrete dynamical systems
- Lefschetz numbers
- Lefschetz zeta function
- Periodic point.
- Topological entropy