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Pré-Publication, Document De Travail Année : 2010

Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms

Résumé

We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).

Dates et versions

hal-00538111 , version 1 (21-11-2010)

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Citer

Sylvain Crovisier, Enrique R. Pujals. Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms. 2010. ⟨hal-00538111⟩
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