Minimal sets of periods for torus maps

Boju Jiang, Jaume Llibre

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39 Citations (Scopus)

Abstract

Let Tr be the r-dimensional torus, and let f: Tr → Tr be a map. If Per(f) denotes the set of periods of f, the minimal set of periods of f, denoted by MPer(f), is defined as ∩g≃f Per(g) where g Tr ← Tr is homotopic to f. First, we characterize the set MPer(f) in terms of the Nielsen numbers of the iterates of f. Second, we distinguish three types of the set MPer(f) and show that for each type and any given dimension r, the variation of MPer(f) is uniformly bounded in a suitable sense. Finally, we classify all the sets MPer(f) for self-maps of the 3-dimensional torus.
Original languageEnglish
Pages (from-to)301-320
JournalDiscrete and Continuous Dynamical Systems
Volume4
Issue number2
Publication statusPublished - 1 Dec 1998

Keywords

  • Minimum set of periods
  • Nielsen fixed point theory
  • Periodic points
  • Three dimensional torus
  • Torus homeomorphisms
  • Torus maps

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    Jiang, B., & Llibre, J. (1998). Minimal sets of periods for torus maps. Discrete and Continuous Dynamical Systems, 4(2), 301-320.