Minimal sets of periods for Morse-Smale diffeomorphisms on non-orientable compact surfaces without boundary

Jaume Llibre, Víctor F. Sirvent

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7 Citations (Scopus)

Abstract

We study the minimal set of (Lefschetz) periods of the C1 Morse-Smale diffeomorphisms on a non-orientable compact surface without boundary inside its class of homology. In fact our study extends to the C1 diffeomorphisms on these surfaces having finitely many periodic orbits, all of them hyperbolic and with the same action on the homology as the Morse-Smale diffeomorphisms. We mainly have two kinds of results. First, we completely characterize the possible minimal sets of periods for the C1 Morse-Smale diffeomorphisms on non-orientable compact surface without boundary of genus g with 1 ≤ g ≤ 9. But the proof of these results provides an algorithm for characterizing the possible minimal sets of periods for the C1 Morse-Smale diffeomorphisms on non-orientable compact surfaces without boundary of arbitrary genus. Second, we study what kind of subsets of positive integers can be minimal sets of periods of the C1 Morse-Smale diffeomorphisms on a non-orientable compact surface without boundary. © 2013 Copyright Taylor and Francis Group, LLC.
Original languageEnglish
Pages (from-to)402-417
JournalJournal of Difference Equations and Applications
Volume19
Issue number3
DOIs
Publication statusPublished - 1 Mar 2013

Keywords

  • Lefschetz number
  • minimal set of periods
  • Morse-Smale diffeomorphism
  • non-orientable compact surfaces
  • set of periods
  • zeta function

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