Partial hyperbolicity far from homoclinic bifurcations |
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Authors: | Sylvain Crovisier |
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Institution: | CNRS – Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, Avenue J.-B. Clément, 93430 Villetaneuse, France |
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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]. |
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Keywords: | MSC: 37C05 37C20 37C29 37C50 37D25 37D30 |
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