Comptes Rendus
no. 10
Dynamical Systems
Recurrence and genericity
[Récurrence et généricité]

Présenté par : Jean-Christophe Yoccoz

Christian Bonatti1 ; Sylvain Crovisier1
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.

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
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/

[1] M.-C. Arnaud Création de connexions en topologie C1, Ergodic Theory Dynamical Systems, Volume 21 (2001), pp. 339-381

[2] Ch. Bonatti, L.J. Dı́az, On maximal transitive sets of generic diffeomorphisms, Publ. Math. Inst. Hautes Études Sci., to appear

[3] C.A. Carballo; C.M. Morales; M.J. Pacı́fico Homoclinic classes for 𝒞 1 -generic vector fields, Ergodic Theory Dynamical Systems, Volume 23 (2003), pp. 1-13

[4] C. Conley Isolated invariant sets and Morse index, CBMS, 38, American Mathematical Society, 1978

[5] S. Hayashi Connecting invariant manifolds and the solution of the C1-stability and Ω-stability conjectures for flows, Ann. of Math., Volume 145 (1997), pp. 81-137

[6] M. Herman Some open problems in dynamical systems, Proceedings of the International Congress of Mathematicians, Vol. II, Berlin, 1998, Doc. Math., Extra Vol. II (1998), pp. 797-808 (electronic)

[7] M. Hurley Attractors: persistence, and density of their basins, Trans. Amer. Math. Soc., Volume 269 (1982), pp. 247-271

[8] C.M. Morales; M.J. Pacı́fico Lyapunopv stability of ω-limit sets, Discrete Contin. Dynam. Systems, Volume 8 (2002), pp. 671-674

[9] C. Pugh The closing lemma, Ergodic Theory Dynamical Systems, Volume 3 (1983), pp. 261-314

[10] C. Pugh; C. Robinson The C1-closing lemma, including Hamiltonians, Ergodic Theory Dynamical Systems, Volume 3 (1983), pp. 261-314

[11] L. Wen; Z. Xia C1-connecting lemmas, Trans. Amer. Math. Soc., Volume 352 (2000), pp. 5213-5230

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