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Partial hyperbolicity far from homoclinic bifurcations
Authors:Sylvain Crovisier
Institution:CNRS – Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, Avenue J.-B. Clément, 93430 Villetaneuse, France
Abstract:We prove that any diffeomorphism of a compact manifold can be C1-approximated by a diffeomorphism which exhibits a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by a diffeomorphism which is partially hyperbolic (its chain-recurrent set splits into partially hyperbolic pieces whose centre bundles have dimensions less or equal to two). We also study in a more systematic way the central models introduced in Crovisier (in press) 10].
Keywords:MSC: 37C05  37C20  37C29  37C50  37D25  37D30
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