Area-Preserving Surface Diffeomorphisms

Abstract

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.

Cited by in corpus (6)

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• Aperiodic invariant continua for surface homeomorphisms
• Homoclinic points for convex billiards
• A diffeomorphism with global dominated splitting can not be minimal
• Homoclinic points of symplectic partially hyperbolic systems with 2D centre