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.
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title = {Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows},
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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] Bonatti C., Viana M., 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] Guckenheimer J., Williams R.F., Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 59-72. | Numdam | MR | Zbl

[4] Hayashi S., 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] Herman M.-R., 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] Hirsch M.W., Pugh C.C., Shub M., Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, Berlin, 1977. | MR | Zbl

[7] Labarca R., Pacífico M.J., Stability of singularity horseshoes, Topology 25 (3) (1986) 337-352. | MR | Zbl

[8] Mañé R., Ergodic Theory and Differential Dynamics, Springer-Verlag, New York, 1987. | MR | Zbl

[9] Morales C.A., Pacífico M.J., Pujals E., 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] Newhouse S., Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9-18. | MR | Zbl

[11] Newhouse S., Hyperbolic Limit Sets, Trans. Amer. Math. Soc. 167 (1972) 125-150. | MR | Zbl

[12] Newhouse S., Lectures on dynamical systems, in: Progr. Math., 8, Birkhäuser, Boston, MA, 1980, pp. 1-114. | MR | Zbl

[13] Oseledets V.I., A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968) 197-231. | Zbl

[14] Palis J., A global view of dynamics and a conjecture on the denseness of finitude of attractors, Asterisque 261 (2000) 339-351. | MR | Zbl

[15] Palis J., On Morse-Smale dynamical systems, Topology 8 (1968) 385-404. | MR | Zbl

[16] Palis J., Smale S., Structural stability theorems, Proc. Amer. Math. Soc. Symp. Pure Math. 14 (1970) 223-232. | MR | Zbl

[17] Palis J., Takens F., Hyperbolicity and Sensitive Chaotic Dynamics of Homoclinic Bifurcations, Cambridge Univ. Press, Cambridge, 1993. | MR | Zbl

[18] Pliss V.A., On a Conjecture of Smale, Differentsial'nye Uravneniya 8 (1972) 268-282. | MR | Zbl

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

[20] Pugh C., An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967) 1010-1021. | MR | Zbl

[21] Pujals E., Sambarino M., 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] Schwartz A.J., 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] Smale S., 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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