@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}, volume = {20}, year = {2003}, pages = {805-841}, doi = {10.1016/S0294-1449(03)00016-7}, mrnumber = {1995503}, zbl = {1045.37006}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 20 (2003) pp. 805-841. doi : 10.1016/S0294-1449(03)00016-7. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_5_805_0/
[1] SRB measures for partially hyperbolic dynamical systems whose central direction is mostly contracting, Israel J. Math. 115 (2000) 157-193. | MR 1749677 | Zbl 0996.37033
, ,[2] C.I. Doering, Persistently transitive vector fields on three manifolds, in: Dynam. Syst. Biff. Theory, Pitman Res. Notes, Vol. 160, 59-89. | MR 907891 | Zbl 0631.58016
[3] Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 59-72. | Numdam | MR 556582 | Zbl 0436.58018
, ,[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 0871.58067
,[5] Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Inst. Hautes Études Sci. Publ. Math. 49 (1979) 5-233. | Numdam | MR 538680 | Zbl 0448.58019
,[6] 583, Springer-Verlag, Berlin, 1977. | MR 501173 | Zbl 0355.58009
, , , Invariant Manifolds, Lecture Notes in Math.,[7] Stability of singularity horseshoes, Topology 25 (3) (1986) 337-352. | MR 842429 | Zbl 0611.58033
, ,[8] | MR 889254 | Zbl 0616.28007
, 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 1649489 | Zbl 0918.58036
, , ,[10] Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9-18. | MR 339291 | Zbl 0275.58016
,[11] Hyperbolic Limit Sets, Trans. Amer. Math. Soc. 167 (1972) 125-150. | MR 295388 | Zbl 0239.58009
,[12] Lectures on dynamical systems, in: Progr. Math., 8, Birkhäuser, Boston, MA, 1980, pp. 1-114. | MR 589590 | Zbl 0444.58001
,[13] A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968) 197-231. | Zbl 0236.93034
,[14] A global view of dynamics and a conjecture on the denseness of finitude of attractors, Asterisque 261 (2000) 339-351. | MR 1755446 | Zbl 1044.37014
,[15] On Morse-Smale dynamical systems, Topology 8 (1968) 385-404. | MR 246316 | Zbl 0189.23902
,[16] Structural stability theorems, Proc. Amer. Math. Soc. Symp. Pure Math. 14 (1970) 223-232. | MR 267603 | Zbl 0214.50702
, ,[17] Hyperbolicity and Sensitive Chaotic Dynamics of Homoclinic Bifurcations, Cambridge Univ. Press, Cambridge, 1993. | MR 1237641 | Zbl 0790.58014
, ,[18] On a Conjecture of Smale, Differentsial'nye Uravneniya 8 (1972) 268-282. | MR 299909 | Zbl 0243.34077
,[19] The closing lemma, Amer. J. Math. 89 (1967) 956-1009. | MR 226669 | Zbl 0167.21803
,[20] An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967) 1010-1021. | MR 226670 | Zbl 0167.21804
,[21] Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Ann. of Math. (2) 151 (3) (2000) 961-1023. | MR 1779562 | Zbl 0959.37040
, ,[22] E. Pujals, M. Sambarino, On the dynamics of dominated splitting, to appear. | Zbl 1178.37032
[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 155061 | Zbl 0116.06803
,[24] Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967) 747-817. | MR 228014 | Zbl 0202.55202
,[25] A. Tahzibi, Stably ergodic systems which are not partially hyperbolic, to appear.