Area-Preserving Surface Diffeomorphisms

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 S² to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem. Research supported in part by National Science Foundation.