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Dynamics of surface homeomorphisms Topological versions of the Leau-Fatou flower theorem and the stable manifold theorem

Frederic Le Roux
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Abstract

The study of the dynamics of a surface homeomorphism in the neighbourhood of an isolated fixed point leads us to the following results. If the fixed point index is greater than 1, a family of attractive and repulsive petals is constructed, generalizing the Leau-Fatou flower theorem in complex dynamics. If the index is less than 1, we get a family of stable and unstable branches, generalizing the stable manifold theorem in hyperbolic dynamics.

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Frederic Le Roux. 2002-10-22. Dynamics of surface homeomorphisms Topological versions of the Leau-Fatou flower theorem and the stable manifold theorem. https://arxiv.org/abs/math/0210344

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