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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65392The 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.In French. 82 pages, 65 figuresDynamical Systems37E30; 37C25Dynamics of surface homeomorphisms Topological versions of the Leau-Fatou flower theorem and the stable manifold theoremtext