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Récurrence et généricité

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Résumé.

Nous montrons un lemme de connexion C 1 pour les pseudo-orbites des difféomorphismes des variétés compactes. Nous explorons alors les conséquences pour les difféomorphismes C 1-génériques. Par exemple, les difféomorphismes conservatifs C 1-génériques (d’une variété connexe) sont transitifs.

Abstract.

We prove a C 1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C 1-generic diffeomorphisms. For instance, C 1-generic conservative diffeomorphisms (on connected manifolds) are transitive.

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Correspondence to Christian Bonatti or Sylvain Crovisier.

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Bonatti, C., Crovisier, S. Récurrence et généricité. Invent. math. 158, 33–104 (2004). https://doi.org/10.1007/s00222-004-0368-1

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