Homoclinic bifurcations and uniform hyperbolicity for three-dimensional flows

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1. [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. Zbl0996.37033MR1749677
2. [2] C.I. Doering, Persistently transitive vector fields on three manifolds, in: Dynam. Syst. Biff. Theory, Pitman Res. Notes, Vol. 160, 59–89. Zbl0631.58016MR907891
3. [3] Guckenheimer J., Williams R.F., Structural stability of Lorenz attractors, Inst. Hautes Études Sci. Publ. Math.50 (1979) 59-72. Zbl0436.58018MR556582
4. [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. Zbl0871.58067
5. [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. Zbl0448.58019MR538680
6. [6] Hirsch M.W., Pugh C.C., Shub M., Invariant Manifolds, Lecture Notes in Math., 583, Springer-Verlag, Berlin, 1977. Zbl0355.58009MR501173
7. [7] Labarca R., Pacífico M.J., Stability of singularity horseshoes, Topology25 (3) (1986) 337-352. Zbl0611.58033MR842429
8. [8] Mañé R., Ergodic Theory and Differential Dynamics, Springer-Verlag, New York, 1987. Zbl0616.28007MR889254
9. [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. Zbl0918.58036MR1649489
10. [10] Newhouse S., Diffeomorphisms with infinitely many sinks, Topology13 (1974) 9-18. Zbl0275.58016MR339291
11. [11] Newhouse S., Hyperbolic Limit Sets, Trans. Amer. Math. Soc.167 (1972) 125-150. Zbl0239.58009MR295388
12. [12] Newhouse S., Lectures on dynamical systems, in: Progr. Math., 8, Birkhäuser, Boston, MA, 1980, pp. 1-114. Zbl0444.58001MR589590
13. [13] Oseledets V.I., A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc.19 (1968) 197-231. Zbl0236.93034
14. [14] Palis J., A global view of dynamics and a conjecture on the denseness of finitude of attractors, Asterisque261 (2000) 339-351. Zbl1044.37014MR1755446
15. [15] Palis J., On Morse–Smale dynamical systems, Topology8 (1968) 385-404. Zbl0189.23902MR246316
16. [16] Palis J., Smale S., Structural stability theorems, Proc. Amer. Math. Soc. Symp. Pure Math.14 (1970) 223-232. Zbl0214.50702MR267603
17. [17] Palis J., Takens F., Hyperbolicity and Sensitive Chaotic Dynamics of Homoclinic Bifurcations, Cambridge Univ. Press, Cambridge, 1993. Zbl0790.58014MR1237641
18. [18] Pliss V.A., On a Conjecture of Smale, Differentsial'nye Uravneniya8 (1972) 268-282. Zbl0243.34077MR299909
19. [19] Pugh C., The closing lemma, Amer. J. Math.89 (1967) 956-1009. Zbl0167.21803MR226669
20. [20] Pugh C., An improved closing lemma and a general density theorem, Amer. J. Math.89 (1967) 1010-1021. Zbl0167.21804MR226670
21. [21] Pujals E., Sambarino M., Homoclinic tangencies and hyperbolicity for surface diffeomorphisms, Ann. of Math. (2)151 (3) (2000) 961-1023. Zbl0959.37040MR1779562
22. [22] E. Pujals, M. Sambarino, On the dynamics of dominated splitting, to appear. Zbl1178.37032
23. [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. Zbl0116.06803MR155061
24. [24] Smale S., Differentiable dynamical systems, Bull. Amer. Math. Soc.73 (1967) 747-817. Zbl0202.55202MR228014
25. [25] A. Tahzibi, Stably ergodic systems which are not partially hyperbolic, to appear. Zbl1052.37019

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