Area-Preserving Surface Diffeomorphisms

We prove some generic properties for $C^r$, $r=1, 2, ..., \infty$, 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 \cite...

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Bibliographic Details
Main Author Xia, Zhihong
Format Journal Article
LanguageEnglish
Published 11.03.2005
Subjects
Mathematics - Dynamical Systems
Mathematics - General Topology
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Summary:We prove some generic properties for $C^r$, $r=1, 2, ..., \infty$, 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 \cite{FL03} on $S^2$ to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.
DOI:10.48550/arxiv.math/0503223