On topological entropy, Lefschetz numbers and Lefschetz zeta functions

Jaume Llibre, Víctor F. Sirvent

Research output: Contribution to journalArticleResearch

Abstract

© 2019 Elsevier B.V. In the present article we give sufficient conditions for C∞ 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 ℓ and the product of spheres of different dimensions.
Original languageEnglish
Article number106906
JournalTopology and its Applications
Volume268
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Entropy
  • Lefschetz numbers
  • Lefschetz zeta function
  • Product of spheres
  • Surfaces
  • Torus

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