Area-Preserving Surface Diffeomorphisms

Details Area-Preserving Surface Diffeomorphisms Area-Preserving Surface Diffeomorphisms

2005-03-11

arxiv.org/abs/math/0503223v1

Mathematics

Dynamical Systems

Scientific paper

10.1007/s00220-005-1514-3

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.

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