Recurrence and genericity

Christian Bonatti; Sylvain Crovisier

doi:10.1016/S1631-073X(03)00203-6

Dynamical Systems

Recurrence and genericity
[Récurrence et généricité]

Présenté par : Jean-Christophe Yoccoz

Christian Bonatti ¹ ; Sylvain Crovisier ¹

¹ Institut de mathématiques de Bourgogne, UMR 5584, Université de Bourgogne, 9, av. A. Savary, BP 47870, 21078 Dijon cedex, France

Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 839-844

Abstract (VO)
Résumé

We prove a C¹-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C¹-generic diffeomorphisms. For instance, C¹-generic conservative diffeomorphisms are transitive.

Nous montrons un lemme de connexion C¹ pour les pseudo-orbites des difféomorphismes des variétés compactes. Nous explorons alors les conséquences pour les difféomorphismes C¹-génériques. Par exemple, les difféomorphismes conservatifs C¹-génériques sont transitifs.

Reçu le : 2003-03-17
Accepté le : 2003-04-01
Publié le : 2003-05-15

DOI : 10.1016/S1631-073X(03)00203-6

Affiliations des auteurs :

Christian Bonatti ¹ ; Sylvain Crovisier ¹

¹ Institut de mathématiques de Bourgogne, UMR 5584, Université de Bourgogne, 9, av. A. Savary, BP 47870, 21078 Dijon cedex, France

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Christian Bonatti; Sylvain Crovisier. Recurrence and genericity. Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 839-844. doi: 10.1016/S1631-073X(03)00203-6

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Cité par

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