@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://archive.numdam.org/item/PMIHES_2003__96__171_0/} }
TY - JOUR AU - Bonatti, Christian AU - Díaz, Lorenzo J. TI - On maximal transitive sets of generic diffeomorphisms JO - Publications Mathématiques de l'IHÉS PY - 2003 SP - 171 EP - 197 VL - 96 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_2003__96__171_0/ LA - en ID - PMIHES_2003__96__171_0 ER -
%0 Journal Article %A Bonatti, Christian %A Díaz, Lorenzo J. %T On maximal transitive sets of generic diffeomorphisms %J Publications Mathématiques de l'IHÉS %D 2003 %P 171-197 %V 96 %I Institut des Hautes Études Scientifiques %U http://archive.numdam.org/item/PMIHES_2003__96__171_0/ %G en %F PMIHES_2003__96__171_0
Bonatti, Christian; Díaz, Lorenzo J. On maximal transitive sets of generic diffeomorphisms. Publications Mathématiques de l'IHÉS, Tome 96 (2003), pp. 171-197. http://archive.numdam.org/item/PMIHES_2003__96__171_0/
[Ab] Generic robustness of a spectral decompositions, to appear in Ann. Scient. Ec. Norm. Sup.. | Numdam | Zbl
,[AS] Nongenericity of -stability, Global Analysis I, Proc. Symp. Pure Math. A.M.S., 14 (1968), 5-8. | MR | Zbl
and ,[Ar] Creation de connexions en topologie , Ergod. Th. Dynam. Syst., 21 (2001), 339-381. | MR | Zbl
,[BD1] Persistent nonhyperbolic transitive diffeomorphims, Ann. Math., 143 (1996), 357-396. | MR | Zbl
and ,[BD2] 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
and ,[BDP] A -generic dichotomy for diffeomorphisms: Weak forms of hyperbolicicity or infinitely many sinks or sources, to appear in Annals of Math.. | MR | Zbl
, and ,[BGLT] Wandering domains for infinitely renormalizable diffeomorphisms of the disk, Proc. Amer. Math. Soc., 122 (2) (1994), 1273-1278. | MR | Zbl
, , and ,[BS] Liapunov stability and adding machines, Ergodic Th. Dynam. Syst., 15 (2) (1995),271-290. | MR | Zbl
and ,[CM] Homoclinic classes and finitude of attractors for vector fields in n-manifolds, reprint (2001). | Zbl
and ,[CMP] Homoclinic classes for -generic vector fields, to appear in Ergodic Th. Dynam. Syst.. | Zbl
, and ,[Ce] Sur les difféomorphismes de la sphère de dimension trois , Lecture Notes in Mathematics 53 1968), pp. xii + 133, Springer-Verlag. | MR | Zbl
,[DPU] Partial hyperbolicity and robust transitivity, Acta Math., 183 (1999), -43. | MR | Zbl
, and ,[DR] Partially hyperbolic and transitive dynamics generated by heteroclinic cycles, Ergodic Th. Dyn. Syst., 25 (2001), 25-76. | MR | Zbl
and ,[DS] Collision, explosion and collapse of homoclinic classes, preprint (2002). | MR | Zbl
and ,[Fr] Necessary conditions for stability of diffeomorphisms, Trans. A.M.S., 158 (1971), 301-308. | MR | Zbl
,[Fu] Strict ergodicity and transformations of the torus, Amer. J. of Math., 83 (1961), 573-601. | MR | Zbl
,[H] Connecting invariant manifolds and the solution of the -stability and -stability conjectures for flows, Ann. of Math., 145 (1997), 81-137. | MR | Zbl
,[Hu] Attractors: persistence and density of their basins, Trans. Amer. Math. Soc., 269 (1982), 247-271. | MR | Zbl
,[Ma] 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] Diffeomorphisms with infinitely many sinks, Topology, 13 (1974), 9-18. | MR | Zbl
,[N2] The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, 50 (1979), 101-151. | Numdam | MR | Zbl
,[PT] Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge Studies in Advanced Mathematics, 35 (1993). | MR | Zbl
and ,[PV] High dimension diffeomorphisms displaying infinitely many sinks, Ann. of Math., 140 (1994), 207-250. | MR | Zbl
and ,[Pu] The closing lemma, Amer. Jour. of Math., 89 (1967), 956-1009. | MR | Zbl
,[Si] R. A 3-dimensional Abraham-Smale example, Proc. A.M.S., 34 (2) (1972), 629-630. | MR | Zbl
,[Sm] Differentiable dynamical systems, Bull. A.M.S., 73 (1967), 747-817. | MR | Zbl
,[Tj] Three dimensional dissipative diffeomorphisms with homoclinic tangencies, Ergod. Th. Dynam. Syst., 21 (2001), 249-302. | MR | Zbl
,