Comptes Rendus
Dynamical Systems
Recurrence and genericity
[Récurrence et généricité]
Comptes Rendus. Mathématique, Volume 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.

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

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, p. 31 | DOI:10.1080/14689367.2023.2230912
  • Davi Obata On the stable ergodicity of diffeomorphisms with dominated splitting, Nonlinearity, Volume 32 (2019) no. 2, p. 445 | DOI:10.1088/1361-6544/aaea93
  • Manseob Lee Asymptotic orbital shadowing property for diffeomorphisms, Open Mathematics, Volume 17 (2019) no. 1, p. 191 | DOI:10.1515/math-2019-0002
  • C. BONATTI SURVEY Towards a global view of dynamical systems, for the C1-topology, Ergodic Theory and Dynamical Systems, Volume 31 (2011) no. 4, p. 959 | DOI:10.1017/s0143385710000891
  • 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
  • Lorenzo J Díaz; Bianca Santoro Collision, explosion and collapse of homoclinic classes, Nonlinearity, Volume 17 (2004) no. 3, p. 1001 | DOI:10.1088/0951-7715/17/3/013
  • Carlos Gutierrez; Benito Pires On Peixoto’s conjecture for flows on non-orientable 2-manifolds, Proceedings of the American Mathematical Society, Volume 133 (2004) no. 4, p. 1063 | DOI:10.1090/s0002-9939-04-07687-7

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