Topological entropy and periods of self-maps on compact manifolds

Juan Luis García Guirao, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


© 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.
Original languageEnglish
Pages (from-to)1337-1347
JournalHouston Journal of Mathematics
Issue number4
Publication statusPublished - 1 Jan 2017


  • Compact manifold
  • Discrete dynamical systems
  • Lefschetz numbers
  • Lefschetz zeta function
  • Periodic point.
  • Topological entropy

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