Periodic points and rotation numbers for area preserving diffeomorphisms of the plane

John Franks*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Let f be an orientation preserving diffeomorphism of R 2 which preserves area. We prove the existence of infinitely many periodic points with distinct rotation numbers around a fixed point of f, provided only that f has two fixed points whose infinitesimal rotation numbers are not both 0. We also show that if a fixed point z of f is enclosed in a "simple heteroclinic cycle" and has a non-zero infinitesimal rotation number r, then for every non-zero rational number p/q in an interval with endpoints 0 and r, there is a periodic orbit inside the heteroclinic cycle with rotation number p/q around z.

Original languageEnglish (US)
Pages (from-to)105-120
Number of pages16
JournalPublications Mathématiques de L'Institut des Hautes Scientifiques
Volume71
Issue number1
DOIs
StatePublished - Dec 1 1990

ASJC Scopus subject areas

  • Mathematics(all)

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