Perturbation de la dynamique de difféomorphismes en topologie $C^1$

Perturbation de la dynamique de difféomorphismes en topologie

C^{1}

Crovisier, Sylvain

Astérisque, no. 354 (2013) , 174 p.

The full text of recent articles is available to journal subscribers only. See the journal's website.

MR: 3136194 | Zbl: 1300.37001

@book{AST_2013__354__R1_0,
     author = {Crovisier, Sylvain},
     title = {Perturbation de la dynamique de diff\'eomorphismes en topologie $C^1$},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {354},
     year = {2013},
     zbl = {1300.37001},
     mrnumber = {3136194},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2013__354__R1_0/}
}

TY  - BOOK
AU  - Crovisier, Sylvain
TI  - Perturbation de la dynamique de difféomorphismes en topologie $C^1$
T3  - Astérisque
PY  - 2013
IS  - 354
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2013__354__R1_0/
LA  - fr
ID  - AST_2013__354__R1_0
ER  -

%0 Book
%A Crovisier, Sylvain
%T Perturbation de la dynamique de difféomorphismes en topologie $C^1$
%S Astérisque
%D 2013
%N 354
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2013__354__R1_0/
%G fr
%F AST_2013__354__R1_0

Crovisier, Sylvain. Perturbation de la dynamique de difféomorphismes en topologie $C^1$. Astérisque, no. 354 (2013), 174 p. http://numdam.org/item/AST_2013__354__R1_0/

References
Cited by

[1] F. Abdenur - « Attractors of generic diffeomorphisms are persistent », Nonlinearity 16 (2003) , no. 1, p. 301-311. | DOI | Zbl | MR

[2] F. Abdenur, « Generic robustness of spectral decompositions », Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 2, p. 213-224. | DOI | Numdam | EuDML | Zbl | MR

[3] F. Abdenur, C. Bonatti & S. Crovisier - « Global dominated splittings and the $C^{1}$ Newhouse phenomenon », Proc. Amer. Math. Soc. 134 (2006), no. 8, p. 2229-2237. | DOI | Zbl | MR

[4] F. Abdenur, C. Bonatti & S. Crovisier, « Nonuniform hyperbolicity for $C^{1}$ -generic diffeomorphisms », Israel J. Math. 183 (2011) , p. 1-60. | DOI | Zbl | MR

[5] F. Abdenur, C. Bonatti, S. Crovisier & L. J. Díaz - « Generic diffeomorphisms on compact surfaces », Fund. Math. 187 (2005), no. 2, p. 127-159. | DOI | EuDML | Zbl | MR

[6] F. Abdenur, C. Bonatti, S. Crovisier, L. J. Díaz & L. Wen - « Periodic points and homoclinic classes », Ergodic Theory Dynam. Systems 27 (2007), p. 1-22. | DOI | Zbl | MR

[7] F. Abdenur, C. Bonatti & L. J. Díaz - « Non-wandering sets with nonempty interiors », Nonlinearity 17 (2004), no. 1, p. 175-191. | DOI | Zbl | MR

[8] F. Abdenur & S. Crovisier - « Transitivity and topological mixing for $C^{1}$ diffeomorphisms », in Essays in mathematics and its applications in honor of Stephen Smale's 80 birthday, Springer, 2012, p. 1-16. | Zbl | MR

[9] R. Abraham & S. Smale - « Nongenericity of $Ω$ -stability », in Global Analysis, Proc. Sympos. Pure Math. , vol. 14, Amer. Math. Soc, 1970, p. 5-8. | DOI | Zbl | MR

[10] R. Abraham & J. Robbin - Transversal mappings and flows, An appendix by Al Kelley, W. A. Benjamin, Inc., 1967. | Zbl | MR

[11] E. Akin, M. Hurley & J. A. Kennedy - « Dynamics of topologically generic homeomorphisms », Mem. Amer. Math. Soc. 164 (2003), no. 783, p. viii+130. | Zbl | MR

[12] D. V. Anosov & A. B. Katok - « New examples in smooth ergodic theory. Ergodic diffeomorphisms », Trans. Moskow Math. Soc. 23 (1970), p. 1-35. | MR | Zbl

[13] N. Aoki - « The set of Axiom $A$ diffeomorphisms with no cycles », Bol. Soc. Brasil. Mat. (N.S.) 23 (1992), no. 1-2, p. 21-65. | DOI | MR | Zbl

[14] M.-C. Arnaud - « Le « closing lemma » en topologie $C^{1}$ », Mém. Soc. Math. Fr. (N.S.) (1998), no. 74, p. vi+120. | Numdam | EuDML | Zbl | MR

[15] M.-C. Arnaud, « Création de connexions en topologie $c^{1}$ », Ergodic Theory Dynam. Systems 31 (2001), p. 339-381. | Zbl | MR

[16] M.-C. Arnaud, « Approximation des ensembles $ω$ -limites des difféomorphismes par des orbites périodiques », Ann. Sci. École Norm. Sup. (4) 36 (2003), no. 2, p. 173-190. | DOI | Numdam | EuDML | Zbl | MR

[17] M. Asaoka - « Hyperbolic sets exhibiting $C^{1}$ -persistent homoclinic tangency for higher dimensions », Proc. Amer. Math. Soc. 136 (2008), no. 2, p. 677-686. | DOI | Zbl | MR

[18] J. Auslander - « Generalized recurrence in dynamical systems », Contributions to Differential Equations 3 (1964), p. 65-74. | Zbl | MR

[19] F. Béguin, S. Crovisier & F. Le Roux - « Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique », Ann. Sci. École Norm. Sup. (4) 40 (2007), no. 2, p. 251-308. | DOI | Numdam | EuDML | Zbl | MR

[20] G. D. Birkhoff - « Nouvelles recherches sur les systèmes dynamiques », Memoriae Pont. Acad. Sci. Novi Lyncaei 1 (1935), p. 85-216. | Zbl | JFM

G. D. Birkhoff - « Nouvelles recherches sur les systèmes dynamiques » Collected Math. Papers, vol. 2, p. 530-659.

[21] J. Bochi & C. Bonatti - « Perturbation of the Lyapunov spectra of periodic orbits », Proc. Lond. Math. Soc. (3) 105 (2012), no. 1, p. 1-48. | DOI | Zbl | MR

[22] C. Bonatti - « Towards a global view of dynamical systems, for the $C^{1}$ -topology », Ergodic Theory Dynam. Systems 31 (2011), p. 959-993. | DOI | Zbl | MR

[23] C. Bonatti & S. Crovisier - « Central manifolds for partially hyperbolic set without strong unstable connections », en préparation. | Zbl

[24] C. Bonatti & S. Crovisier, « Récurrence et généricité », Invent. Math. 158 (2004), no. 1, p. 33-104. | DOI | Zbl | MR

[25] C. Bonatti, S. Crovisier, L. J. Díaz & N. Gourmelon - « Internai perturbations of homoclinic classes : non-domination, cycles, and self-replication », Ergodic Theory Dynam. Systems 33 (2013), no. 3, p. 739-776. | DOI | Zbl | MR

[26] C. Bonatti, S. Crovisier, N. Gourmelon & R. Potrie - « Tame dynamics and robust transitivity », prépublication ArXiv : 1112.1002, à paraître à Trans. Amer. Math. Soc. | Zbl

[27] C. Bonatti, S. Crovisier, G. M. Vago & A. Wilkinson - « Local density of diffeomorphisms with large centralizers », Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), no. 6, p. 925-954. | DOI | Numdam | EuDML | Zbl | MR

[28] C. Bonatti, S. Crovisier & A. Wilkinson - « $C^{1}$ -generic conservative diffeomorphisms have trivial centralizer », J. Mod. Dyn. 2 (2008) , no. 2, p. 359-373. | DOI | Zbl | MR

[29] C. Bonatti, S. Crovisier & A. Wilkinson, « The $C^{1}$ generic diffeomorphism has trivial centralizer », Publ. Math. Inst. Hautes Études Sci. (2009), no. 109, p. 185-244. | DOI | Numdam | EuDML | Zbl | MR

[30] C. Bonatti & L. J. Díaz - « Persistent nonhyperbolic transitive diffeomorphisms », Ann. Math. (2) 143 (1995), p. 357-396. | Zbl | MR

[31] C. Bonatti & L. J. Díaz, « Connexions hétéroclines et généricité d'une infinité de puits et de sources », Ann. Sci. École Norm. Sup. (4) 32 (1999), no. 1, p. 135-150. | DOI | Numdam | EuDML | Zbl | MR

[32] C. Bonatti & L. J. Díaz, « On maximal transitive sets of generic diffeomorphisms », Publ. Math. Inst. Hautes Études Sci. (2003), no. 96, p. 171-197 | DOI | Numdam | EuDML | Zbl | MR

C. Bonatti & L. J. Díaz, « On maximal transitive sets of generic diffeomorphisms », Publ. Math. Inst. Hautes Études Sci. no. 96, p. 171-197 (2003). | DOI | Numdam | EuDML | Zbl | MR

[33] C. Bonatti & L. J. Díaz, « Robust heterodimensional cycles and $C^{1}$ -generic dynamics », J. Inst. Math. Jussieu 7 (2008), no. 3, p. 469-525. | DOI | Zbl | MR

[34] C. Bonatti & L. J. Díaz, « Abundance of $C^{1}$ -robust homoclinic tangencies », Trans. Amer. Math. Soc. 364 (2012), no. 10, p. 5111-5148. | DOI | Zbl | MR

[35] C. Bonatti & L. J. Díaz, « Fragile cycles », J. Differential Equations 252 (2012), no. 7, p. 4176-4199. | DOI | Zbl | MR

[36] C. Bonatti, L. J. Díaz & S. Kiriki - « Stabilization of heterodimensional cycles », Nonlinearity 25 (2012), no. 4, p. 931-960. | DOI | Zbl | MR

[37] C. Bonatti, L. J. Díaz & E. R. Pujals - « A $C^{1}$ -generic dichotomy for diffeomorphisms : weak forms of hyperbolicity or infinitely many sinks or sources », Ann. of Math. (2) 158 (2003), no. 2, p. 355-418. | DOI | Zbl | MR

[38] C. Bonatti, L. J. Díaz, E. R. Pujals & J. Rocha - « Robustly transitive sets and heterodimensional cycles », in Geometric methods in dynamics. I, Astérisque, vol. 286, Soc. Math. France, 2003, p. 187-222. | Numdam | Zbl | MR

[39] C. Bonatti, L. J. Díaz & M. Viana - Dynamics beyond uniform hyperbolicity, Encyclopaedia Math. Sci., vol. 102, Springer-Verlag, 2005. | Zbl | MR

[40] C. Bonatti, S. Gan, M. Li & D. Yang - « Lyapunov stable classes and essential attractors », en préparation.

[41] C. Bonatti, S. Gan & L. Wen - « On the existence of non-trivial homoclinic classes », Ergodic Theory Dynam. Systems 27 (2007) , p. 1473-1508. | DOI | Zbl | MR

[42] C. Bonatti, S. Gan & D. Yang - « On the hyperbolicity of homoclinic classes », Discrete Contin. Dyn. Syst. 25 (2009) , no. 4, p. 1143-1162. | DOI | Zbl | MR

[43] C. Bonatti, N. Gourmelon & T. Vivier - « Perturbations of the derivative along periodic orbits », Ergodic Theory Dynam. Systems 26 (2006), p. 1307-1337. | DOI | Zbl | MR

[44] C. Bonatti, M. Li & D. Yang - « On the existence of attractors », Trans. Amer. Math. Soc. 365 (2013), no. 3, p. 1369-1391. | DOI | Zbl | MR

[45] C. Bonatti & M. Viana - « SRB measures for partially hyperbolic systems whose central direction is mostly contracting », Israel J. Math. 115 (2000), p. 157-193. | DOI | Zbl | MR

[46] R. Bowen - « Periodic points and measures for Axiom $A$ diffeomorphisms », Trans. Amer. Math. Soc. 154 (1971), p. 377-397. | Zbl | MR

[47] R. Bowen, Equilibrium states and the ergodic theory of Axiom $A$ diffeomorphisms, Lecture Notes in Math., vol. 470, Springer-Verlag, 1975. | Zbl | MR

[48] L. Burslem - « Centralizers of partially hyperbolic diffeomorphisms », Ergod. Th. Dynam. Sys. 24 (2004) , p. 55-87. | DOI | Zbl | MR

[49] C. M. Carballo, C. A. Morales & M. J. Pacifico - « Maximal transitive sets with singularities for generic C1 vector fields », Bol. Soc. Brasil. Mat. (N.S.) 31 (2000), no. 3, p. 287-303. | DOI | Zbl | MR

[50] M. Carvalho - « Sinaĭ-Ruelle-Bowen measures for $N$ -dimensional [ $N$ dimensions] derived from Anosov diffeomorphisms », Ergodic Theory Dynam. Systems 13 (1993), no. 1, p. 21-44. | DOI | Zbl | MR

[51] C. Conley - Isolated invariant sets and the Morse index, CCBMS Reg. Conf. Ser. Math., vol. 38, Amer. Math. Soc., 1978. | Zbl | MR

[52] S. Crovisier - « Periodic orbits and chain-transitive sets of $C^{1}$ -diffeomorphisms », Publ. Math. Inst. Hautes Études Sci. (2006), no. 104, p. 87-141. | Numdam | DOI | EuDML | Zbl | MR

[53] S. Crovisier, « Perturbation of $C^{1}$ -diffeomorphisms and generic conservative dynamics on surfaces », in Dynamique des difféomorphismes conservatifs des surfaces : un point de vue topologique, Panor. Synthèse, vol. 21, Soc. Math. France, 2006, p. 1-33. | Zbl | MR

[54] S. Crovisier, « Birth of homoclinic intersections : a model for the central dynamics of partially hyperbolic systems », Ann. of Math. (2) 172 (2010), no. 3, p. 1641-1677. | DOI | Zbl | MR

[55] S. Crovisier, « Partial hyperbolicity far from homoclinic bifurcations », Adv. Math. 226 (2011), no. 1, p. 673-726. | DOI | Zbl | MR

[56] S. Crovisier & E. Pujals - « Essential hyperbolicity versus homoclinic bifurcations », prépublication ArXiv : 1011.3836.

[57] S. Crovisier, M. Sambarino & D. Yang - « Partial Hyperbolicity and Homoclinic Tangencies », prépublication ArXiv : 1103.0869 ; à paraître à J. Eur. Math. Soc. | Zbl | MR

[58] L. J. Díaz & A. Gorodetski - « Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes », Ergodic Theory Dynam. Systems 29 (2009), no. 5, p. 1479-1513. | DOI | Zbl | MR

[59] L. J. Díaz, E. R. Pujals & R. Ures - « Partial hyperbolicity and robust transitivity », Acta Math. 183 (1999), no. 1, p. 1-43. | DOI | Zbl | MR

[60] T. Fisher - « Trivial centralizers for axiom $A$ diffeomorphisms », Nonlinearity 21 (2008), no. 11, p. 2505-2517. | DOI | Zbl | MR

[61] M. D. Foreman, D. J. Rudolph & B. Weiss - « On the conjugacy relation in ergodic theory », C. R. Math. Acad. Sci. Paris 343 (2006), no. 10, p. 653-656. | DOI | Zbl | MR

[62] J. Franks - « Necessary conditions for stability of diffeomorphisms », Trans. Amer. Math. Soc. 158 (1971), p. 301-308. | DOI | Zbl | MR

[63] S. Gan - « A generalized shadowing lemma », Discrete Contin. Dyn. Syst. 8 (2002), no. 3, p. 627-632. | DOI | Zbl | MR

[64] S. Gan, « Horseshoe and entropy for $C^{1}$ surface diffeomorphisms », Nonlinearity 15 (2002), no. 3, p. 841-848. | DOI | Zbl | MR

[65] S. Gan & L. Wen - « Heteroclinic cycles and homoclinic closures for generic diffeomorphisms », J. Dynam. Differential Equations 15 (2003), no. 2-3, p. 451-471, (volume spécial à l'occasion des 70 ans de Victor A. Pliss). | DOI | Zbl | MR

[66] É. Ghys - « Groups acting on the circle », Enseign. Math. (2) 47 (2001), no. 3-4, p. 329-407. | Zbl | MR

[67] N. Gourmelon - « A Franks' lemma that preserves invariant manifolds », prépublication ArXiv : 0912.1121. | DOI | Zbl | MR

[68] N. Gourmelon, « Adapted metrics for dominated splittings », Ergodic Theory Dynam. Systems 27 (2007), p. 1839-1849. | DOI | Zbl | MR

[69] N. Gourmelon, « Generation of homoclinic tangencies by $C^{1}$ -perturbations », Discrete Contin. Dyn. Syst. 26 (2010), no. 1, p. 1-42. | DOI | Zbl | MR

[70] C. Gutierrez - « A counter-example to a $C^{2}$ closing lemma », Ergodic Theory Dynam. Systems 7 (1987), no. 4, p. 509-530. | DOI | Zbl | MR

[71] C. Gutierrez, « On $C^{r}$ -closing for flows on $2$ -manifolds », Nonlinearity 13 (2000), no. 6, p. 1883-1888. | DOI | Zbl | MR

[72] C. Gutierrez, « On the $C^{r}$ -closing lemma the geometry of differential equations and dynamical Systems », Comput. Appl. Math. 20 (2001), no. 1-2, p. 179-186. | Zbl | MR

[73] S. Hayashi - « Diffeomorphisms in $F^{1} (M)$ satisfy Axiom $A$ », Ergodic Theory Dynam. Systems 12 (1992), p. 233-253. | DOI | Zbl | MR

[74] S. Hayashi, « Connecting invariant manifolds and the solution of the $C^{1}$ stability and $Ω$ -stability conjectures for flows », Ann. of Math. (2) 145 (1997), no. 1, p. 81-137. | DOI | Zbl | MR

S. Hayashi, « Connecting invariant manifolds and the solution of the $C^{1}$ stability and $ω$ -stability conjectures for flows », Ann. of Math. (2) 150 (1999), p. 353-356. | DOI | EuDML | Zbl | MR

[75] S. Hayashi, « A $C^{1}$ make or break lemma », Bol. Soc. Brasil. Mat. (N.S.) 31 (2000), no. 3, p. 337-350. | DOI | Zbl | MR

[76] S. Hayashi, « Stability of dynamical systems », Sugaku Expositions 14 (2001), no. 1, p. 15-29, traduction de Sugaku 50 (1998), no. 2, p. 149-162. | Zbl | MR

[77] M. R. Herman - Sur les courbes invariantes par les difféomorphismes de l'anneau, Astérisque, vol. 103-104, Soc. Math. France, 1983. | Numdam | Zbl | MR

[78] M. R. Herman, « Différentiabilité optimale et contre-exemples à la fermeture en topologie $C^{\infty}$ des orbites récurrentes de flots hamiltoniens », C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 1, p. 49-51. | Zbl | MR

[79] M. R. Herman, « Exemples de flots hamiltoniens dont aucune perturbation en topologie $C^{\infty}$ n'a d'orbites périodiques sur un ouvert de surfaces d'énergies », C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 13, p. 989-994. | MR | Zbl

[80] M. R. Herman, « Some open problems in dynamical systems », in Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math., 1998, p. 797-808. | EuDML | Zbl | MR

[81] M. W. Hirsch - Differential topology, Grad. Texts in Math., vol. 33, Springer-Verlag, 1994. | MR

[82] M. W. Hirsch, C. C. Pugh & M. Shub - Invariant manifolds, Lecture Notes in Math., vol. 583, Springer-Verlag, 1977. | Zbl | MR

[83] M. Hurley - « Attractors : persistence, and density of their basins », Trans. Amer. Math. Soc. 269 (1982), no. 1, p. 247-271. | DOI | Zbl | MR

[84] A. Katok - « Lyapunov exponents, entropy and periodic orbits for diffeomorphisms », Publ. Math. Inst. Hautes Études Sci. (1980), no. 51, p. 137-173. | DOI | Numdam | EuDML | Zbl | MR

[85] A. Katok & B. Hasselblatt - Introduction to the modern theory of dynamical systems, Encyclopaedia Math. Appl., vol. 54, Cambridge Univ. Press, 1995. | MR | Zbl

[86] N. Kopell - « Commuting diffeomorphisms », in Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, p. 165-184. | DOI | Zbl | MR

[87] I. Kupka - « Contribution à la théorie des champs génériques », Contributions to Differential Equations 2 (1963), p. 457-484. | MR | Zbl

[88] K. Kuratowski - Topology. Vol. II, Academic Press/PWN/Polish Sci. Publishers, 1968. | MR

[89] F. Ledrappier - « Quelques propriétés des exposants caractéristiques », in École d'été de probabilités de Saint-Flour, XII - 1982, Lecture Notes in Math., vol. 1097, Springer, 1984, p. 305-396. | DOI | Zbl | MR

[90] G. Liao, M. Viana & J. Yang - « The Entropy Conjecture for Diffeomorphisms away from Tangencies », prépublication ArXiv : 1012.0514. | Zbl | MR

[91] S. T. Liao - « An existence theorem for periodic orbits », Acta Sci. Nat. Univ. Pekin. (1979), no. 1, p. 1-20. | MR

[92] S. T. Liao, « An extension of the $C^{1}$ closing lemma », Beijn Daxne Xuebao 2 (1979), p. 1-41. | MR

[93] S. T. Liao, « Obstruction sets. I » ,Acta Math. Sinica 23 (1980), no. 3, p. 411-453. | Zbl | MR

[94] S. T. Liao, « On the stability conjecture », Chinese Ann. Math. 1 (1980), no. 1, p. 9-30. | MR | Zbl

[95] S. T. Liao, « Obstruction sets. II », Beijing Daxue Xuebao (1981), no. 2, p. 1-36. | MR

[96] S. T. Liao, Qualitative theory of differentiable dynamical systems, China Science Press, 1996, traduction en anglais des articles précédents. | Zbl | MR

[97] J. H. Mai - « A simpler proof of $C^{1}$ closing lemma », Sci. Sinica Ser. A 29 (1986), no. 10, p. 1020-1031. | Zbl | MR

[98] R. Mañé - « Contributions to the stability conjecture », Topology 17 (1978), no. 4, p. 383-396. | DOI | Zbl | MR

[99] R. Mañé, « An ergodic closing lemma », Ann. of Math. (2) 116 (1982), no. 3, p. 503-540. | DOI | Zbl | MR

[100] R. Mañé, « Oseledec's theorem from the generic viewpoint », in Proceedings of the International Congress of Mathematicians, (Warsaw, 1983), vol. 1-2, PWN, 1984, p. 1269-1276. | Zbl | MR

[101] R. Mañé, « Hyperbolicity, sinks and measure in one-dimensional dynamics », Comm. Math. Phys. 100 (1985), no. 4, p. 495-524. | DOI | Zbl | MR

R. Mañé, « Hyperbolicity, sinks and measure in one-dimensional dynamics », Comm. Math. Phys. 112 (1987), p. 721-724. | DOI | Zbl | MR

[102] R. Mañé, Ergodic theory and differentiable dynamics, Ergeb. Math.Grenzgeb. (3), vol. 8, Springer-Verlag, 1987. | Zbl | MR

[103] R. Mañé, « On the creation of homoclinic points », Publ. Math. Inst. Hautes Études Sci. (1987), no. 66, p. 139-159. | Numdam | EuDML | Zbl | MR

[104] R. Mañé, « A proof of the $C^{1}$ stability conjecture », Publ. Math. Inst. Hautes Études Sci. (1987), no. 66, p. 161-210. | Numdam | EuDML | Zbl | MR

[105] Marie-Claude, C. Bonatti & S. Crovisier - « Dynamiques symplectiques génériques », Ergodic Theory Dynam. Systems 25 (2005), p. 1401-1436. | DOI | Zbl | MR

[106] C. A. Morales & M. J. Pacifico - « Lyapunov stability of $ω$ -limit sets », Discrete Contin. Dyn. Syst. 8 (2002), no. 3, p. 671-674. | DOI | Zbl | MR

[107] C. G. Moreira - « There are no $C^{1}$ -stable intersections of regular Cantor sets », Acta Math. 206 (2011), no. 2, p. 311-323. | DOI | Zbl | MR

[108] J. Moser - Stable and random motions in dynamical systems, Ann. of Math. Stud., vol. 77, Princeton University Press, 1973. | Zbl | MR

[109] J. Munkres - « Obstructions to the smoothing of pieeewise-differentiable homeomorphisms », Ann. of Math. (2) 72 (1960), p. 521-554. | DOI | Zbl | MR

[110] S. E. Newhouse - « Nondensity of axiom $A (a)$ on $S^{2}$ », in Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, p. 191-202. | DOI | Zbl | MR

[111] S. E. Newhouse, « Hyperbolic limit sets », Trans. Amer. Math. Soc. 167 (1972), p. 125-150. | DOI | Zbl | MR

[112] S. E. Newhouse, « Diffeomorphisms with infinitely many sinks », Topology 13 (1974), p. 9-18. | DOI | Zbl | MR

[113] S. E. Newhouse, « Quasi-elliptic periodic points in conservative dynamical systems », Amer. J. Math. 99 (1977), no. 5, p. 1061-1087. | DOI | Zbl | MR

[114] S. E. Newhouse, « The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms », Publ. Math. Inst. Hautes Études Sci. (1979), no. 50, p. 101- 151. | DOI | Numdam | EuDML | Zbl | MR

[115] S. E. Newhouse, « Lectures on dynamical systems », in Dynamical systems (C.I.M.E. Summer School, Bressanone, 1978), Progr. Math., vol. 8, Birkhäuser Boston, 1980, p. 1-114. | Zbl | MR

[116] S. E. Newhouse & J. Palis - « Cycles and bifurcation theory », in Trois études en dynamique qualitative, Astérisque, vol. 31, Soc. Math. France, 1976, p. 43-140. | Numdam | Zbl | MR

[117] F. Oliveira - « On the generic existence of homoclinic points », Ergodic Theory Dynam. Systems 7 (1987), no. 4, p. 567-595. | DOI | Zbl | MR

[118] F. Oliveira, « On the $C^{\infty}$ genericity of homoclinic orbits », Nonlinearity 13 (2000), no. 3, p. 653-662. | DOI | Zbl | MR

[119] J. Palis, - « A note on $Ω$ -stability », in Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., 1970, p. 221-222. | DOI | MR | Zbl

[120] J. Palis, « On the $C^{1} Ω$ -stability conjecture », Publ. Math. Inst. Hautes Études Sci. (1987), no. 66, p. 211-215. | Numdam | EuDML | Zbl | MR

[121] J. Palis, « On the contribution of Smale to dynamical systems », in From Topology to Computation : Proceedings of the Smalefest (Berkeley, CA, 1990), Springer, 1993, p. 165-178. | DOI | Zbl | MR

[122] J. Palis, « A global view of dynamics and a conjecture on the denseness of finitude of attractors », in Géométrie complexe et systèmes dynamiques (Orsay, 1995), Astérisque, vol. 261, Soc. Math. France, 2000, p. xiii-xiv, 335-347. | Numdam | Zbl | MR

[123] J. Palis, « A global perspective for non-conservative dynamics », Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 4, p. 485-507. | DOI | Numdam | EuDML | Zbl | MR

[124] J. Palis, « Open questions leading to a global perspective in dynamics », Nonlinearity 21 (2008), no. 4, p. T37-T43. | DOI | Zbl | MR

[125] J. Palis & W. De Melo - Geometric theory of dynamical systems, an introduction, Springer-Verlag, 1982. | Zbl | MR

[126] J. Palis & C. Pugh - « Fifty problems in dynamical systems », in Dynamical systems (Warwick 1914), Lecture Notes in Math., vol. 468, Springer, 1975, Edited by J. Palis and C. C. Pugh, p. 345-353. | DOI | Zbl

[127] J. Palis, C. Pugh, M. Shub & D. Sullivan - « Genericity theorems in topological dynamics », in Dynamical systems (Warwick 1974), Lecture Notes in Math., vol. 468, Springer, 1975, p. 241-250. | DOI | Zbl | MR

[128] J. Palis & S. Smale - « Structural stability theorems », in Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc, 1970, p. 223-231. | DOI | Zbl | MR

[129] J. Palis & F. Takens - Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Stud. Adv. Math., vol. 35, Cambridge Univ. Press, 1993, Fractal dimensions and infinitely many attractors. | Zbl | MR

[130] J. Palis & M. Viana - « High dimension diffeomorphisms displaying infinitely many periodic attractors », Ann. of Math. (2) 140 (1994), no. 1, p. 207-250. | DOI | Zbl | MR

[131] J. Palis & J.-C. Yoccoz - « Centralizers of Anosov diffeomorphisms on tori », Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 1, p. 99-108. | DOI | Numdam | EuDML | Zbl | MR

[132] J. Palis & J.-C. Yoccoz, « Rigidity of centralizers of diffeomorphisms », Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 1, p. 81-98. | DOI | Numdam | EuDML | Zbl | MR

[133] M. M. Peixoto - « Structural stability on two-dimensional manifolds », Topology 1 (1962), p. 101-120. | DOI | Zbl | MR

M. M. Peixoto - « Structural stability on two-dimensional manifolds », Topology 2 (1963), p. 179-180. | DOI | Zbl | MR

[134] Y. Pesin - « Characteristic Ljapunov exponents and smooth ergodic theory », Russian Math. Surveys 324 (1977), no. 4, p. 55-114. | DOI | Zbl

[135] D. Pixton - « Planar homoclinic points », J. Differential Equations 44 (1982), no. 3, p. 365-382. | DOI | Zbl | MR

[136] V. A. Pliss - « On a conjecture of Smale », Differencial'nye Uravnenija 8 (1972), p. 268-282. | Zbl | MR

[137] R. V. Plykin - « Sources and sinks of $A$ -diffeomorphisms of surfaces », Mat. Sb. (N.S.) 94 (136) (1974), p. 243-264, 336. | EuDML | Zbl | MR

[138] H. Poincaré - « Sur le problème des trois corps et les équations de la dynamique », Acta Math. 13 (1890), p. 1-270. | JFM

[139] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, tome III, Gauthier-Villars, 1899. | MR | JFM

[140] R. Potrie - « Wild Milnor attractors accumulated by lower dimensional dynamics », prépublication ArXiv : 1106.3741. | DOI | Zbl | MR

[141] R. Potrie, « Generic bi-Lyapunov stable homoclinic classes », Nonlinearity 23 (2010), no. 7, p. 1631-1649. | DOI | Zbl | MR

[142] R. Potrie & M. Sambarino- « Codimension one generic homoclinic classes with interior », Bull. Braz. Math. Soc. (N.S.) 41 (2010), no. 1, p. 125-138. | DOI | Zbl | MR

[143] C. C. Pugh - « The closing lemma », Amer. J. Math. 89 (1967), p. 956-1009. | DOI | Zbl | MR

[144] C. C. Pugh, « An improved closing lemma and a general density theorem », Amer. J. Math. 89 (1967), p. 1010-1021. | DOI | Zbl | MR

[145] C. C. Pugh, « On arbitrary sequences of isomorphisms in $R^{m} \to R^{m}$ », Trans. Amer. Math. Soc. 184 (1973), p. 387-400. | Zbl | MR

[146] C. C. Pugh, « Against the $C^{2}$ closing lemma », J. Differential Equations 17 (1975), p. 435-443. | DOI | Zbl | MR

[147] C. C. Pugh, « A special $C^{r}$ closing lemma », in Geometric dynamics (Rio de Janeiro, 1981), Lecture Notes in Math., vol. 1007, Springer, 1983, p. 636-650. | DOI | Zbl | MR

[148] C. C. Pugh, « The $C^{1 + α}$ hypothesis in Pesin theory », Publ. Math. Inst. Hautes Études Sci. (1984), no. 59, p. 143-161. | DOI | Numdam | EuDML | Zbl | MR

[149] C. C. Pugh, « The $C^{1}$ connecting lemma », J. Dynam. Differential Equations 4 (1992), no. 4, p. 545-553. | DOI | Zbl | MR

[150] C. C. Pugh & C. Robinson - « The $C^{1}$ closing lemma, including Hamiltonians », Ergodic Theory Dynam. Systems 3 (1983), no. 2, p. 261-313. | Zbl | MR

[151] C. C. Pugh, M. Shub & A. Wilkinson - « Hölder foliations », Duke Math. J. 86 (1997), no. 3, p. 517-546. | DOI | Zbl | MR

[152] E. R. Pujals - « On the density of hyperbolicity and homoclinic bifurcations for 3D-diffeomorphisms in attracting regions », Discrete Contin.Dyn. Syst. 16 (2006), no. 1, p. 179-226. | DOI | Zbl | MR

[153] E. R. Pujals, « Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets », Discrete Contin. Dyn. Syst. 20 (2008), no. 2, p. 335-405. | DOI | Zbl | MR

[154] E. R. Pujals, « Some simple questions related to the $C^{r}$ stability conjecture », Nonlinearity 21 (2008), no. 11, p. T233-T237. | DOI | Zbl | MR

[155] E. R. Pujals & F. Rodriguez Hertz - « Critical points for surface diffeomorphisms », J. Mod. Dyn. 1 (2007), no. 4, p. 615-648. | DOI | Zbl | MR

[156] E. R. Pujals & M. Sambarino - « Homoclinic tangencies and hyperbolicity for surface diffeomorphisms », Ann. of Math. (2) 151 (2000), no. 3, p. 961-1023. | DOI | EuDML | Zbl | MR

[157] E. R. Pujals & M. Sambarino, « Integrability on codimension one dominated splitting », Bull. Braz. Math. Soc. (N.S.) 38 (2007), no. 1, p. 1-19. | DOI | Zbl | MR

[158] E. R. Pujals & M. Sambarino, « Density of hyperbolicity and tangencies in sectional dissipative regions », Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, p. 1971-2000. | DOI | Numdam | EuDML | Zbl | MR

[159] E. R. Pujals & M. Sambarino, « On the dynamics of dominated splitting », Ann. of Math. (2) 169 (2009), no. 3, p. 675-739. | DOI | Zbl | MR

[160] J. W. Robbin - « A structural stability theorem », Ann. of Math. (2) 94 (1971), p. 447-493. | DOI | Zbl | MR

[161] R. C. Robinson - « Generic properties of conservative systems », Amer. J. Math. 92 (1970), no. 1-2, p. 562-603, et p. 897-906. | DOI | Zbl | MR

[162] R. C. Robinson, « Closing stable and unstable manifolds on the two sphere », Proc. Amer. Math. Soc. 41 (1973), p. 299-303. | DOI | Zbl | MR

[163] R. C. Robinson, « $C^{r}$ structural stability implies Kupka-Smale », in Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971), Academic Press, 1973, p. 443-449. | MR | Zbl

[164] R. C. Robinson, « Structural stability of $C^{1}$ diffeomorphisms », J. Differential Equations 22 (1976), no. 1, p. 28-73. | DOI | MR | Zbl

[165] R. C. Robinson, Dynamical systems, second éd., Studies in Advanced Mathematics, CRC Press, 1999, Stability, symbolic dynamics, and chaos. | Zbl | MR

[166] N. Romero- « Persistence of homoclinic tangencies in higher dimensions », Ergodic Theory Dynam. Systems 15 (1995), no. 4, p. 735-757. | DOI | Zbl | MR

[167] A. Rovella & M. Sambarino - « The $C^{1}$ closing lemma for generic $C^{1}$ endomorphisms », Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 6, p. 1461-1469. | DOI | Numdam | Zbl | MR

[168] K. Shinohara - « An example of $C^{1}$ -generically wild homoclinic classes with index deficiency », Nonlinearity 24 (2011), no. 7, p. 1961-1974. | DOI | Zbl | MR

[169] K. Shinohara, « On the index problem of $C^{1}$ -generic wild homoclinic classes in dimension three », Discrete Contin. Dyn. Syst. 31 (2011), no. 3, p. 913-940. | DOI | Zbl | MR

[170] M. Shub - « Topological transitive diffeomorphism on $t^{4}$ », in Differential Equations and Dynamical Systems, Lecture Notes in Math., vol. 206, Springer, 1971, p. 39-40.

[171] M. Shub, « Structurally stable diffeomorphisms are dense », Bull. Amer. Math. Soc. 78 (1972), p. 817-818. | DOI | MR | Zbl

[172] M. Shub, « Stability and genericity for diffeomorphisms », in Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971), Academic Press, 1973, p. 493-514. | Zbl | MR

[173] M. Shub, Stabilité globale des systèmes dynamiques, Astérisque, vol. 56, Soc. Math. France, 1978. | Numdam | Zbl | MR

[174] K. Sigmund - « Generic properties of invariant measures for Axiom $A$ diffeomorphisms », Invent. Math. 11 (1970), p. 99-109. | DOI | EuDML | Zbl | MR

[175] C. P. Simon - « A $3$ -dimensional Abraham-Smale example », Proc. Amer. Math. Soc. 34 (1972), p. 629-630. | MR | Zbl

[176] S. Smale - « Morse inequalities for a dynamical system », Bull. Amer. Math. Soc. 66 (1960), p. 43-49. | DOI | Zbl | MR

[177] S. Smale, « Dynamical systems and the topological conjugacy problem for diffeomorphisms », in Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, 1963, p. 490-496. | Zbl | MR

[178] S. Smale, « Stable manifolds for differential equations and diffeomorphisms », Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), p. 97-116. | Numdam | EuDML | Zbl | MR

[179] S. Smale, « Diffeomorphisms with many periodic points », in Differential and Combinatorial Topology, Princeton Univ. Press, 1965, p. 63-80. | MR | Zbl

[180] S. Smale, « Structurally stable systems are not dense », Amer. J. Math. 88 (1966), p. 491-496. | DOI | Zbl | MR

[181] S. Smale, « Differentiable dynamical Systems », Bull. Amer. Math. Soc. 73 (1967), p. 747-817. | DOI | Zbl | MR

[182] S. Smale, « The $Ω$ -stability theorem », in Global Analysis, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc, 1970, p. 289-297. | DOI | Zbl | MR

[183] S. Smale, « Stability and genericity in dynamical systems », in Séminaire Bourbaki Vol. 1969/70, Lecture Notes in Math., vol. 180, Springer, 1971, exp. 374, p. 177-185. | DOI | Numdam | EuDML | Zbl

[184] S. Smale, « Dynamics retrospective : great problems, attempts that failed », Phys. D 51 (1991), no. 1-3, p. 267-273, Nonlinear science : the next decade (Los Alamos, NM, 1990). | DOI | MR | Zbl

[185] S. Smale, « Mathematical problems for the next century », Math. Intelligencer 20 (1998), no. 2, p. 7-15. | DOI | MR | Zbl

[186] F. Takens - « On Zeeman's tolerance stability conjecture », in Manifolds - Amsterdam 1970 (Proc. Nuffic Summer School), Lecture Notes in Math., vol. 197, Springer, 1971, p. 209-219. | DOI | Zbl | MR

[187] F. Takens, « Tolerance stability », in Dynamical systems -Warwick 1974 (Proc. Sympos. Appl. Topology and Dynamical Systems, Univ. Warwick, Coventry, 1973/1974 ; presented to E. C. Zeeman on his fiftieth birthday), Lecture Notes in Math., vol. 468, Springer, 1975, p. 293-304. | Zbl | MR

[188] Y. Togawa - « Generic Morse-Smale diffeomorphisms have only trivial symmetries », Proc. Amer. Math. Soc. 65 (1977), no. 1, p. 145-149. | DOI | Zbl | MR

[189] Y. Togawa, « Centralizers of $C^{1}$ -diffeomorphisms », Proc. Amer. Math. Soc. 71 (1978), no. 2, p. 289-293. | MR | Zbl

[190] D. Turaev - « Maps close to the identity and universal maps in the Newhouse domain », prépublication ArXiv : 1009.0858vl. | DOI | Zbl | MR

[191] L. Wen - « The $C^{1}$ closing lemma for endomorphisms with finitely many singularities », Proc. Amer. Math. Soc. 114 (1992), no. 1, p. 217-223. | Zbl | MR

[192] L. Wen, « Homoclinic tangencies and dominated splittings », Nonlinearity 15 (2002), no. 5, p. 1445-1469. | DOI | MR | Zbl

[193] L. Wen, « A uniform $C^{1}$ connecting lemma », Discrete Contin. Dyn. Syst. 8 (2002), no. 1, p. 257-265. | DOI | Zbl | MR

[194] L. Wen, « Generic diffeomorphisms away from homoclinic tangencies and hetero-dimensional cycles », Bull. Braz. Math. Soc. (N.S.) 35 (2004), no. 3, p. 419-452. | DOI | Zbl | MR

[195] L. Wen, « The selecting lemma of Liao », Discrete Contin. Dyn. Syst. 20 (2008), no. 1, p. 159-175. | DOI | Zbl | MR

[196] L. Wen & Z. Xia - « A basic $C^{1}$ perturbation theorem », J. Differential Equations 154 (1999), no. 2, p. 267-283. | DOI | Zbl | MR

[197] L. Wen & Z. Xia, « $C^{1}$ connecting lemmas », Trans. Amer. Math. Soc. 352 (2000), no. 11, p. 5213-5230. | DOI | Zbl | MR

[198] D. Yang, S. Gan & L. Wen - « Minimal non-hyperbolicity and index-completeness », Discrete Contin. Dyn. Syst. 25 (2009), no. 4, p. 1349-1366. | DOI | Zbl | MR

[199] J. Yang - « Ergodic measures far away from tangencies », prépublication IMPA A629 (2009).

[200] J. Yang, « Lyapunov stable chain recurrent classes », prépublication ArXiv : 0712.0514.

[201] J. Yang, « Newhouse phenomenon and homoclinic classes », Ergodic Theory Dynam. Systems 31 (2011), no. 5, p. 1537-1562. | DOI | MR | Zbl

[202] J.-C. Yoccoz - « Travaux de Herman sur les tores invariants », Astérisque (1992), no. 206, p. Exp. No. 754, 4, 311-344, Séminaire Bourbaki, Vol. 1991/92. | Numdam | EuDML | Zbl | MR

[203] J.-C. Yoccoz, « Introduction to hyperbolic dynamics », in Real and complex dynamical systems (Hillerød, 1993), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 464, Kluwer Acad. Publ., 1995, p. 265-291. | DOI | Zbl | MR

[204] E. Zehnder - « Homoclinic points near elliptic fixed points », Comm. Pure Appl. Math. 26 (1973), p. 131-182. | DOI | Zbl | MR