Connexions hétéroclines et généricité d'une infinité de puits et de sources
Bonatti, Christian ; Díaz, Lorenzo
Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999), p. 135-150 / Harvested from Numdam
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@article{ASENS_1999_4_32_1_135_0,
     author = {Bonatti, Christian and D\'\i az, Lorenzo J.},
     title = {Connexions h\'et\'eroclines et g\'en\'ericit\'e d'une infinit\'e de puits et de sources},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {32},
     year = {1999},
     pages = {135-150},
     doi = {10.1016/s0012-9593(99)80012-3},
     mrnumber = {2000e:37015},
     zbl = {0944.37012},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_1999_4_32_1_135_0}
}

Bonatti, Christian; Díaz, Lorenzo. Connexions hétéroclines et généricité d'une infinité de puits et de sources. Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999) pp. 135-150. doi : 10.1016/s0012-9593(99)80012-3. http://gdmltest.u-ga.fr/item/ASENS_1999_4_32_1_135_0/

[AS] R. Abraham et S. Smale, Nongenericity of &Ω-stability, Global Analysis I, Proc. Symp. Pure Math. A.M.S., 14, p. 5-8, 1968. | MR 42 #6867 | Zbl 0215.25102

[BD] R. Ch. Bonatti et L. J. Díaz, Persistence of transitive diffeomorphims, Ann. Math., 143, p. 367-396, 1995.

[BV] R. Ch. Bonatti et M. Viana, SRB measures for partially hyperbolic attractors : the contracting case, à paraître dans Israel J. of Math.

[D] R. L. J. Díaz, Robust nonhyperbolic dynamics at heterodimensional cycles, Erg. Th. and Dyn. Sys., 15, p. 291-315, 1995. | Zbl 0831.58035

[DPU] R. L. J. Díaz, E. Pujals et R. Ures, Partial hyperbolicity and robust transitivity, prepublication PUC-Rio 1998.

[F] J. Franks, Necessary conditions for the stability of diffeomorphisms, Trans. A.M.S., 158, p. 301-308, 1971. | MR 44 #1042 | Zbl 0219.58005

[H] R. S. Hayashi, Connecting invariant manifolds and the solution of the C1-stability and &Ω-stability conjectures for flows, Ann. of Math., 145, p. 81-137, 1997. | Zbl 0871.58067

[HPS] R. M. Hirsch, C. Pugh et M. Shub, Invariant manifolds, Lecture Notes in Math., p. 583, Springer Verlag, 1977. | Zbl 0355.58009

[M1] R. R. Mañé, Contributions to the C1-stability conjecture, Topology, 17, p. 386-396, 1978. | MR 84b:58061 | Zbl 0405.58035

[M2] R. R. Mañé, An ergodic closing lemma, Ann. Math., 116, p. 541-558, 1982. | MR 84f:58070 | Zbl 0511.58029

[N1] R. S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13, p. 9-18, 1974. | MR 49 #4051 | Zbl 0275.58016

[N2] R. S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, 50, p. 101-151, 1979. | Numdam | MR 82e:58067 | Zbl 0445.58022

[PT] R. J. Palis et F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Studies in Advanced Mathematics, p. 35, 1993. | MR 94h:58129 | Zbl 0790.58014

[PV] R. J. Palis et M. Viana, High dimensional diffeomorphisms displaying infinitely many sinks, Ann. of Math., 140, p. 207-250, 1994. | Zbl 0817.58004

[R] R. N. Romero, Persistence of homoclinic tangencies in higher dimension, Erg. Th. and Dyn. Sys., 15, p. 735-759, 1995. | MR 96e:58118 | Zbl 0833.58020

[Si1] R. C. Simon, A 3-dimensional Abrahame-Smale example Proc. A.M.S. vol 34 (2), p. 629-630 1972. | Zbl 0259.58006

[Si2] R. C. Simon, On a classification of a Baire set of diffeomorphisms Bull. A.M.S. vol 77 (5), p. 783-787, 1971. | MR 44 #2242 | Zbl 0227.58005

[S] R. S. Smale, Differentiable dynamical systems, Bull. A.M.S., 73, p. 147-817, 1967. | MR 37 #3598

[U] R. R. Ures, Abundance of hyperbolicity in the C1-topology, Ann. Scient. École Norm. Sup. Paris, 4e série, 28, p. 747-760, 1995. | Numdam | MR 96i:58135 | Zbl 0989.37013

[YA] R. J. A. Yorke et K. T. Alligood, Cascades of period doubling bifurcations : a pre-requisite for horseshoes, Bull. A.M.S., 9, p. 319-322, 1983. | Zbl 0541.58039