Sets of periods for piecewise monotone tree maps

Ll Alsedà, D. Juher, P. Mumbrú

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)

Abstract

We study the set of periods of tree maps f : T → T which are monotone between any two consecutive points of a fixed periodic orbit P. This set is characterized in terms of some integers which depend only on the combinatorics of f|p and the topological structure of T. In particular, a type p ≥ 1 of P is defined as a generalization of the notion introduced by Baldwin in his characterization of the set of periods of star maps. It follows that there exists a divisor k of the period of P such that if the set of periods of f is not finite then it contains either all the multiples of kp or an initial segment of the kp≥ Baldwin's ordering, except for a finite set which is explicitly bounded. Conversely, examples are given where f has precisely these sets of periods.
Original languageEnglish
Pages (from-to)311-341
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume13
DOIs
Publication statusPublished - 1 Jan 2003

Keywords

  • Periodic orbits
  • Set of periods
  • Tree maps

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