A Stable/Unstable "Manifold" Theorem for Area Preserving Homeomorphisms of Two Manifolds

Stewart Baldwin, Edward E. Slaminka
1990 Proceedings of the American Mathematical Society  
The stable/unstable manifold theorem for hyperbolic diffeomorphisms has proven to be of extreme importance in differentiable dynamics. We prove a stable/unstable "manifold" theorem for area preserving homeomorphisms of orientable two manifolds having isolated fixed points of index less than 1. The proof relies upon the concept of free modification which was first developed by Morton Brown for homeomorphisms of two manifolds and later extended by Pelikan and Slaminka for area preserving homeomorphisms of two manifolds.
doi:10.2307/2048225 fatcat:vyv4m6wjmjhcjmzdkhf5h33utm