Global periodicity conditions for maps and recurrences via normal forms

Anna Cima, Armengol Gasull, Víctor Mañosa

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

We face the problem of characterizing the periodic cases in parametric families of rational diffeomorphisms of k, where is R or C, having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two- and three-dimensional classes of polynomial or rational maps. In particular, we find the global periodic cases for several Lyness-type recurrences. © 2013 World Scientific Publishing Company.
Original languageEnglish
Article number1350182
JournalInternational Journal of Bifurcation and Chaos
Volume23
Issue number11
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Globally periodic recurrences
  • Linearization
  • Lyness-type recurrences
  • Normal forms
  • Periodic maps
  • Rational parametrizations

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