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Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems

We prove a conjecture of J. Palis: any diffeomorphism of a compact manifold can be C1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection. ----- Cr'eation d'intersection homoclines : un mod`ele pour la dynamique centrale des syst`emes partiellement hyperboliques. Nous montrons une conjecture de J. Palis : tout diff'eomorphisme d'une vari'et'e compacte peut ^etre approch'e en topologie C1 par un diff'eomorphisme Morse-Smale ou par un diff'eomorphisme ayant une intersection homocline transverse.

preprint2010arXivOpen access
Sylvain Crovisier
math.DS
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Sylvain Crovisier

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