Attractors and time averages for random maps
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 3, pp. 307-369.
@article{AIHPC_2000__17_3_307_0,
     author = {Ara\'ujo, V{\'\i}tor},
     title = {Attractors and time averages for random maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {307--369},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {3},
     year = {2000},
     mrnumber = {1771137},
     zbl = {0974.37036},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2000__17_3_307_0/}
}
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Araújo, Vítor. Attractors and time averages for random maps. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 3, pp. 307-369. http://www.numdam.org/item/AIHPC_2000__17_3_307_0/

[1] Alves J.F., Bonatti C., Viana M., SRB measures for partially hyperbolic diffeomorphisms, the expanding case, in preparation.

[2] Benedicks M., Moeckel R., An attractor for certain Hénon maps, Preprint E.T.H., Zurich.

[3] Brin M., Pesin Ya., Partially hyperbolic dynamical systems, Izv. Akad. Nauk. SSSR 1 (1974) 170-212. | MR | Zbl

[4] Bonatti C., Díaz L.J., Connexions heterocliniques et genericité d'une infinité de puits ou de sources, Preprint PUC-Rio, 1998.

[5] Bonatti C., Díaz L.J., Pujals E., Genericity of Newhouse's phenomenon vs. dominated splitting, in preparation.

[6] Bonatti C., Viana M., SRB measures for partially hyperbolic systems whose central direction is mostly contracting, Preprint IMPA, 1997. | MR

[7] Colli E., Infinitely many coexisting strange attractors, Annales de l'Institut Henri Poincaré - Analyse Non-Linéaire (accepted for publication). | Numdam | Zbl

[8] Díaz L.J., Pujals E., Ures R., Normal hyperbolicity and robust transitivity, Preprint PUC-Rio, 1997.

[9] Fomaess J., Sibony N., Random iterations of rational functions, Ergodic Theory Dynamical Systems 11 (4) (1991) 687-708. | MR | Zbl

[10] Gambaudo J.-M., Tresser C., Diffeomorphisms with infinitely many strange attractors, J. Complexity 6 (1990) 409-416. | MR | Zbl

[11] Gonchenko S.V., Shil'Nikov L.P., Turaev D.V., Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits, Chaos 6 ( 1 ) (1996) 15-31. | MR | Zbl

[12] Grayson M., Pugh C., Shub M., Stably ergodic diffeomorphisms, Annals of Math. 140 (1994) 295-329. | MR | Zbl

[13] Munroe M.E., Introduction to Measure and Probability, Addison-Wesley, Cambridge, MA, 1953. | MR | Zbl

[14] Mañé R., Contributions to the stability conjecture, Topology 17 (4) (1978) 383-396. | MR | Zbl

[15] Mañé R., Ergodic Theory and Differentiable Dynamics, Springer, Berlin, 1987. | MR | Zbl

[16] Newhouse S., Non-density of axion A(a) on S2, Proc. AMS Symp. Pure Math. 14 (1970) 191-202. | Zbl

[17] Newhouse S., Diffeomorphisms with infinitely many sinks, Topology 13 (1974) 9- 18. | MR | Zbl

[18] Newhouse S., The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES 50 (1979) 101-151. | Numdam | MR | Zbl

[19] Petersen K., Ergodic Theory, Cambridge Studies in Advanced Math., No. 2, Cambridge, 1983. | MR | Zbl

[20] Palis J., A global view of dynamics and a conjecture on the denseness of finitude of attractors, Astérisque (1998). | Numdam | MR | Zbl

[21] Palis J., De Melo W., Geometric Theory of Dynamical Systems, Springer, New York, 1982. | MR | Zbl

[22] Palis J., Takens F., Hyperbolic and Sensitive Chaotic Dynamics at Homoclinic Bifurcations, Cambridge Studies in Advanced Math., No. 35, Cambridge, 1993. | MR | Zbl

[23] Palis J., Viana M., High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals of Math. 140 (1994) 207-250. | MR | Zbl

[24] Pesin Ya., Sinai Ya., Gibbs measures for partially hyperbolic attractors, Ergodic Theory Dynamical Systems 2 (1982) 417-438. | MR | Zbl

[25] Romero N., Persistence of homoclinic tangencies in higher dimensions, Ergodic Theory Dynamical Systems 15 (1995) 735-757. | MR | Zbl

[26] Shub M., Global Stability of Dynamical Systems, Springer, New York, 1987. | MR | Zbl

[27] Takens F., Partially hyperbolic fixed points, Topology 10 (1971) 137-151. | MR | Zbl

[28] Takens F., Heteroclinic attractors: time averages and moduli of topological conjugacy, Bol. Soc. Bras. Mat. 25 (1) (1994) 107-120. | MR | Zbl

[29] Tedeschini-Lalli L., Yorke J.A., How often do simple dynamical processes have infinitely many coexisting sinks, Comm. Math. Phys. 106 (1986) 635-657. | MR | Zbl

[30] Viana M., Global attractors and bifurcations, in: Broer H.W., van Gils S.A., Hoveijn I., Takens F. (Eds.), Nonlinear Dynamical Systems and Chaos Progress in Nonlinear Partial Differential Equations and Applications (PNLDE No. 19), Birkhäuser, 1996, pp. 299-324. | MR | Zbl

[31] Viana M., Dynamics: A probabilistic and geometric perspective, in: Proceedings ICM, Documenta Mathematica, 1998. | MR | Zbl