On maximal transitive sets of generic diffeomorphisms

Bonatti, Christian; Díaz, Lorenzo J.

Bonatti, Christian ; Díaz, Lorenzo J.

Publications Mathématiques de l'IHÉS, Tome 96 (2003), pp. 171-197.

MR Zbl | 6 citations dans Numdam

@article{PMIHES_2003__96__171_0,
     author = {Bonatti, Christian and D{\'\i}az, Lorenzo J.},
     title = {On maximal transitive sets of generic diffeomorphisms},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {171--197},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {96},
     year = {2003},
     mrnumber = {1985032},
     zbl = {1032.37011},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2003__96__171_0/}
}

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Bonatti, Christian; Díaz, Lorenzo J. On maximal transitive sets of generic diffeomorphisms. Publications Mathématiques de l'IHÉS, Tome 96 (2003), pp. 171-197. http://www.numdam.org/item/PMIHES_2003__96__171_0/

Bibliographie
Cité par

[Ab] F. Abdenur, Generic robustness of a spectral decompositions, to appear in Ann. Scient. Ec. Norm. Sup.. | Numdam | Zbl

[AS] R. Abraham and S. Smale, Nongenericity of $ω$ -stability, Global Analysis I, Proc. Symp. Pure Math. A.M.S., 14 (1968), 5-8. | MR | Zbl

[Ar] M.-C. Arnaud, Creation de connexions en topologie $C^{1}$ , Ergod. Th. Dynam. Syst., 21 (2001), 339-381. | MR | Zbl

[BD1] Ch. Bonatti and L. J. Díaz, Persistent nonhyperbolic transitive diffeomorphims, Ann. Math., 143 (1996), 357-396. | MR | Zbl

[BD2] Ch. Bonatti and L. J. Díaz, Connexions hétéroclines et généricité d'une infinité de puits ou de sources, Ann. Scient. Ec. Norm. Sup., 4e série, t32 (1999), 135-150. | Numdam | Zbl

[BDP] Ch. Bonatti, L. J. Díaz and E. R. Pujals, A $C^{1}$ -generic dichotomy for diffeomorphisms: Weak forms of hyperbolicicity or infinitely many sinks or sources, to appear in Annals of Math.. | MR | Zbl

[BGLT] Ch. Bonatti, J.-M. Gambaudo, J.-M. Lion and Ch. Tresser, Wandering domains for infinitely renormalizable diffeomorphisms of the disk, Proc. Amer. Math. Soc., 122 (2) (1994), 1273-1278. | MR | Zbl

[BS] J. Buescu and I. Stewart, Liapunov stability and adding machines, Ergodic Th. Dynam. Syst., 15 (2) (1995),271-290. | MR | Zbl

[CM] C. Carballo and C. Morales, Homoclinic classes and finitude of attractors for vector fields in n-manifolds, reprint (2001). | Zbl

[CMP] C. Carballo, C. Morales and M. J. Pacífico, Homoclinic classes for $C^{1}$ -generic vector fields, to appear in Ergodic Th. Dynam. Syst.. | Zbl

[Ce] J. Cerf, Sur les difféomorphismes de la sphère de dimension trois $(Γ_{4} = 0)$ , Lecture Notes in Mathematics 53 1968), pp. xii + 133, Springer-Verlag. | MR | Zbl

[DPU] L. J. Díaz, E. R. Pujals and R. Ures, Partial hyperbolicity and robust transitivity, Acta Math., 183 (1999), -43. | MR | Zbl

[DR] L. J. Díaz and J. Rocha, Partially hyperbolic and transitive dynamics generated by heteroclinic cycles, Ergodic Th. Dyn. Syst., 25 (2001), 25-76. | MR | Zbl

[DS] L. J. Díaz and B. Santoro, Collision, explosion and collapse of homoclinic classes, preprint (2002). | MR | Zbl

[Fr] J. Franks, Necessary conditions for stability of diffeomorphisms, Trans. A.M.S., 158 (1971), 301-308. | MR | Zbl

[Fu] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. of Math., 83 (1961), 573-601. | MR | Zbl

[H] S. Hayashi, Connecting invariant manifolds and the solution of the $C^{1}$ -stability and $ω$ -stability conjectures for flows, Ann. of Math., 145 (1997), 81-137. | MR | Zbl

[Hu] M. Hurley, Attractors: persistence and density of their basins, Trans. Amer. Math. Soc., 269 (1982), 247-271. | MR | Zbl

[Ma] R. Mane, An ergodic closing lemma, Ann. of Math., 116 (1982), 503-540. | MR | Zbl

[Mi] J. W. MILNOR, Topology from differential view point, Charlottesville, The University Press of Virginia, 1965.

[N1] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, 13 (1974), 9-18. | MR | Zbl

[N2] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, 50 (1979), 101-151. | Numdam | MR | Zbl

[PT] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Studies in Advanced Mathematics, 35 (1993). | MR | Zbl

[PV] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many sinks, Ann. of Math., 140 (1994), 207-250. | MR | Zbl

[Pu] C. Pugh, The closing lemma, Amer. Jour. of Math., 89 (1967), 956-1009. | MR | Zbl

[Si] R. C. Simon, A 3-dimensional Abraham-Smale example, Proc. A.M.S., 34 (2) (1972), 629-630. | MR | Zbl

[Sm] S. Smale, Differentiable dynamical systems, Bull. A.M.S., 73 (1967), 747-817. | MR | Zbl

[Tj] J. C. Tatjer, Three dimensional dissipative diffeomorphisms with homoclinic tangencies, Ergod. Th. Dynam. Syst., 21 (2001), 249-302. | MR | Zbl