C1 self-maps on closed manifolds with finitely many periodic points all of them hyperbolic

Jaume Llibre, Víctor F. Sirvent

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2016, Akademie ved Ceske Republiky. All rights reserved. Let X be a connected closed manifold and f a self-map on X. We say that f is almost quasi-unipotent if every eigenvalue λ of the map f*k (the induced map on the k-th homology group of X) which is neither a root of unity, nor a zero, satisfies that the sum of the multiplicities of λ as eigenvalue of all the maps f*k with k odd is equal to the sum of the multiplicities of λ as eigenvalue of all the maps f*k with k even. We prove that if f is C1 having finitely many periodic points all of them hyperbolic, then f is almost quasi-unipotent.
Original languageEnglish
Pages (from-to)83-90
JournalMathematica Bohemica
Volume141
Issue number1
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • Almost quasi-unipotent map
  • Differentiable map
  • Hyperbolic periodic point
  • Lefschetz number
  • Lefschetz zeta function
  • Quasi-unipotent map

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