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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00203-6/

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Xueming Hui Topological pressure for conservative $C^{1}$ -diffeomorphisms with no dominated splitting, Dynamical Systems, Volume 39 (2024) no. 1, pp. 31-61 | DOI:10.1080/14689367.2023.2230912 | Zbl:7792701
Davi Obata On the stable ergodicity of diffeomorphisms with dominated splitting, Nonlinearity, Volume 32 (2019) no. 2, pp. 445-463 | DOI:10.1088/1361-6544/aaea93 | Zbl:1410.37030
Manseob Lee Asymptotic orbital shadowing property for diffeomorphisms, Open Mathematics, Volume 17 (2019), pp. 191-201 | DOI:10.1515/math-2019-0002 | Zbl:1436.37033
C. Bonatti Towards a global view of dynamical systems, for the $C^{1}$ -topology, Ergodic Theory and Dynamical Systems, Volume 31 (2011) no. 4, pp. 959-993 | DOI:10.1017/s0143385710000891 | Zbl:1256.37006
Enrique R. Pujals; Martin Sambarino Homoclinic Bifurcations, Dominated Splitting, and Robust Transitivity, Volume 1 (2006), p. 327 | DOI:10.1016/s1874-575x(06)80029-9
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