Area-preserving surface diffeomorphisms

Zhihong Xia*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We prove some generic properties for C r , r = 1,2,. . .,∞, area-preserving diffeomorphism on compact surfaces. The main result is that the union of the stable (or unstable) manifolds of hyperbolic periodic points are dense in the surface. This extends the result of Franks and Le Calvez [10] on S 2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.

Original languageEnglish (US)
Pages (from-to)723-735
Number of pages13
JournalCommunications in Mathematical Physics
Volume263
Issue number3
DOIs
StatePublished - May 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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