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Proceedings of the American Mathematical Society

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A stable/unstable ``manifold'' theorem for area preserving homeomorphisms of two manifolds


Authors: Stewart Baldwin and Edward E. Slaminka
Journal: Proc. Amer. Math. Soc. 109 (1990), 823-828
MSC: Primary 58F15; Secondary 58F10
MathSciNet review: 1013963
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-1013963-4
Keywords: Fixed point, index, stable and unstable manifold, area preserving
Article copyright: © Copyright 1990 American Mathematical Society