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  on S 2 to general surfaces. The proof uses the theory of prime ends and Lefschetz fixed point theorem.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics