Dynamical Systems
Recurrence and genericity
[Récurrence et généricité]

Présenté par : Jean-Christophe Yoccoz

Bonatti, Christian1 ; Crovisier, Sylvain1
1 Institut de mathématiques de Bourgogne, UMR 5584, Université de Bourgogne, 9, av. A. Savary, BP 47870, 21078 Dijon cedex, France
Comptes Rendus. Mathématique, Tome 336 (2003) no. 10, pp. 839-844.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00203-6
Bonatti, Christian 1 ; Crovisier, Sylvain 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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Bonatti, Christian; Crovisier, Sylvain. Recurrence and genericity. Comptes Rendus. Mathématique, Tome 336 (2003) no. 10, pp. 839-844. doi : 10.1016/S1631-073X(03)00203-6. http://www.numdam.org/articles/10.1016/S1631-073X(03)00203-6/

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