Real dynamics of integrable birational maps

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Abstract

We begin by studying the dynamic generated by iteration of birational maps in ℝk with k - 1 independent rational first integrals. We prove that each level curve can be desingularized and compactified being homeomorphic to a finite union of disjoint circles and open intervals. Furthermore, the map can be extended homeomorphically in a natural way to this space. After, we focus our attention in the case that the map has a rational invariant measure and we see that in most cases the orbit of a point or it is periodic or it fulfills densely some connected components of its corresponding level set. Some applications in dimension two and three are presented. © Springer Basel AG 2011.
Original languageEnglish
Pages (from-to)247-275
JournalQualitative Theory of Dynamical Systems
Volume10
DOIs
Publication statusPublished - 1 Dec 2011

Keywords

  • Birational maps
  • Circle maps
  • Difference equations
  • Discrete dynamical systems
  • First integrals
  • Integrable maps
  • Lie-symmetries
  • Periodic orbits
  • Rotation numbers

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