A stable/unstable “manifold” theorem for area preserving homeomorphisms of two manifolds

Baldwin, Stewart; Slaminka, Edward E.

doi:10.1090/S0002-9939-1990-1013963-4

A stable/unstable “manifold” theorem for area preserving homeomorphisms of two manifolds
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by Stewart Baldwin and Edward E. Slaminka PDF

Proc. Amer. Math. Soc. 109 (1990), 823-828 Request permission

Abstract:

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.

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