@article{AIHPC_2003__20_5_805_0, author = {Arroyo, Aubin and Rodriguez Hertz, Federico}, title = {Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {805--841}, publisher = {Elsevier}, volume = {20}, number = {5}, year = {2003}, doi = {10.1016/S0294-1449(03)00016-7}, mrnumber = {1995503}, zbl = {1045.37006}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S0294-1449(03)00016-7/} }
TY - JOUR AU - Arroyo, Aubin AU - Rodriguez Hertz, Federico TI - Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 805 EP - 841 VL - 20 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S0294-1449(03)00016-7/ DO - 10.1016/S0294-1449(03)00016-7 LA - en ID - AIHPC_2003__20_5_805_0 ER -
%0 Journal Article %A Arroyo, Aubin %A Rodriguez Hertz, Federico %T Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 805-841 %V 20 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S0294-1449(03)00016-7/ %R 10.1016/S0294-1449(03)00016-7 %G en %F AIHPC_2003__20_5_805_0
Arroyo, Aubin; Rodriguez Hertz, Federico. Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 5, pp. 805-841. doi : 10.1016/S0294-1449(03)00016-7. http://archive.numdam.org/articles/10.1016/S0294-1449(03)00016-7/
[1] SRB measures for partially hyperbolic dynamical systems whose central direction is mostly contracting, Israel J. Math. 115 (2000) 157-193. | MR | Zbl
, ,[2] C.I. Doering, Persistently transitive vector fields on three manifolds, in: Dynam. Syst. Biff. Theory, Pitman Res. Notes, Vol. 160, 59-89. | MR | Zbl
[3] Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 59-72. | Numdam | MR | Zbl
, ,[4] Connecting invariant manifolds and the solution of the C1 stability and Ω-stability conjectures for flows, Ann. of Math. (2) 145 (1) (1997) 81-137. | Zbl
,[5] Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. 49 (1979) 5-233. | Numdam | MR | Zbl
,[6] 583, Springer-Verlag, Berlin, 1977. | MR | Zbl
, , , Invariant Manifolds, Lecture Notes in Math.,[7] Stability of singularity horseshoes, Topology 25 (3) (1986) 337-352. | MR | Zbl
, , , Ergodic Theory and Differential Dynamics, Springer-Verlag, New York, 1987. |[9] On C1 robust singular transitive sets for three-dimensional flows, C. R. Acad. Sci. Paris Sér. I Math. 326 (1) (1998) 81-86. | MR | Zbl
, , ,[10] Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9-18. | MR | Zbl
,[11] Hyperbolic Limit Sets, Trans. Amer. Math. Soc. 167 (1972) 125-150. | MR | Zbl
,[12] Lectures on dynamical systems, in: Progr. Math., 8, Birkhäuser, Boston, MA, 1980, pp. 1-114. | MR | Zbl
,[13] A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968) 197-231. | Zbl
,[14] A global view of dynamics and a conjecture on the denseness of finitude of attractors, Asterisque 261 (2000) 339-351. | Numdam | MR | Zbl
,[15] On Morse-Smale dynamical systems, Topology 8 (1968) 385-404. | MR | Zbl
,[16] Structural stability theorems, Proc. Amer. Math. Soc. Symp. Pure Math. 14 (1970) 223-232. | MR | Zbl
, ,[17] Hyperbolicity and Sensitive Chaotic Dynamics of Homoclinic Bifurcations, Cambridge Univ. Press, Cambridge, 1993. | MR | Zbl
, ,[18] On a Conjecture of Smale, Differentsial'nye Uravneniya 8 (1972) 268-282. | MR | Zbl
,[19] The closing lemma, Amer. J. Math. 89 (1967) 956-1009. | MR | Zbl
,[20] An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967) 1010-1021. | MR | Zbl
,[21] Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Ann. of Math. (2) 151 (3) (2000) 961-1023. | EuDML | MR | Zbl
, ,[22] E. Pujals, M. Sambarino, On the dynamics of dominated splitting, to appear. | Zbl
[23] A generalization of a Poincaré-Bendixon theorem to closed two dimensional manifolds, Amer. J. Math. 85 (1963) 453-458, Errata, ibid 85 (1963) 753. | MR | Zbl
,[24] Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967) 747-817. | MR | Zbl
,[25] A. Tahzibi, Stably ergodic systems which are not partially hyperbolic, to appear.
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