Universal dynamics in a neighborhood of a generic elliptic periodic point

V. Gelfreich, D. Turaev

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We show that a generic area-preserving two-dimensional map with an elliptic periodic point is Cω-universal, i.e., its renormalized iterates are dense in the set of all real-analytic symplectic maps of a two-dimensional disk. The results naturally extend onto Hamiltonian and volume-preserving flows.

Original languageEnglish
Pages (from-to)159-164
Number of pages6
JournalRegular and Chaotic Dynamics
Volume15
Issue number2
DOIs
StatePublished - 1 Jan 2010
Externally publishedYes

Keywords

  • Area-preserving map
  • Exponentially small splitting
  • Hamiltonian system
  • Homoclinic tangency
  • KAM theory
  • Newhouse phenomenon
  • Volume-preserving flow
  • Wild hyperbolic set

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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