Periodic points of Hamiltonian surface diffeomorphisms

John Franks*, Michael Handel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S2 provided the diffeomorphism has at least three fixed points. In addition we show that up to isotopy relative to its fixed point set, every orientation preserving di eomorphism F: S→S of a closed orientable surface has a normal form. If the fixed point set is finite this is just the Thurston normal form.

Original languageEnglish (US)
Pages (from-to)713-756
Number of pages44
JournalGeometry and Topology
Volume7
DOIs
StatePublished - 2003

Keywords

  • Geodesic lamination
  • Hamiltonian diffeomorphism
  • Periodic points

ASJC Scopus subject areas

  • Geometry and Topology

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