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

2002/10/22 by Frederic Le Roux, Roux, Frederic Le
Mathematics · #37C25 #37E30 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C25 #msc:37E30

paper · pdf · doi:10.48550/arxiv.math/0210344

In French. 82 pages, 65 figures

arxiv created 2002/10/22 · arxiv updated 2009/11/30

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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