Topological entropy and periods of self–maps on compact manifolds
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Matemática AplicadaSponsors
The first author of this work was partially supported by MINECO grant number MTM2014-51891-P and Fundación Séneca de la Región de Murcia grant number 19219/PI/14. The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant number 2014SGR-568, and the grants FP7-PEOPLE-2012-IRSES 318999 and 316338.Publication date
2017Publisher
Department of Mathematics, University of HoustonBibliographic Citation
Guirao, J. L. G., & Llibre, J. (2017). Topological entropy and periods of self-maps on compact manifolds. Houston Journal of Mathematics, 43(4),1337-1347Keywords
Compact manifoldTopological entropy
Discrete dynamical systems
Lefschetz numbers
Lefschetz zeta function
Periodic point
Abstract
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 x Sm, CPn and HPn we improve the previous sufficient conditions.
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