English

Area-Preserving Surface Diffeomorphisms

Dynamical Systems 2009-11-11 v1 General Topology

Abstract

We prove some generic properties for CrC^r, r=1,2,...,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 S2S^2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.

Keywords

Cite

@article{arxiv.math/0503223,
  title  = {Area-Preserving Surface Diffeomorphisms},
  author = {Zhihong Xia},
  journal= {arXiv preprint arXiv:math/0503223},
  year   = {2009}
}