Random perturbations and statistical properties of Hénon-like maps
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 5, pp. 713-752.
@article{AIHPC_2006__23_5_713_0,
     author = {Benedicks, Michael and Viana, Marcelo},
     title = {Random perturbations and statistical properties of {H\'enon-like} maps},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {713--752},
     publisher = {Elsevier},
     volume = {23},
     number = {5},
     year = {2006},
     doi = {10.1016/j.anihpc.2004.10.013},
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     zbl = {1131.37033},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.013/}
}
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Benedicks, Michael; Viana, Marcelo. Random perturbations and statistical properties of Hénon-like maps. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 5, pp. 713-752. doi : 10.1016/j.anihpc.2004.10.013. http://archive.numdam.org/articles/10.1016/j.anihpc.2004.10.013/

[1] J.F. Alves, V. Araújo, Stochastic stability for robust classes of non-uniformly expanding maps, Astérisque.

[2] Andronov A., Pontryagin L., Systèmes grossiers, Dokl. Akad. Nauk USSR 14 (1937) 247-251. | Zbl

[3] Araújo V., Attractors and time averages for random maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 307-369. | Numdam | MR | Zbl

[4] Arnold L., Random Dynamical Systems, Springer-Verlag, 1998. | MR | Zbl

[5] A. Avila, C.G. Moreira, Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative, Astérisque. | Numdam | MR | Zbl

[6] Baladi V., Viana M., Strong stochastic stability and rate of mixing for unimodal maps, Ann. Sci. École Norm. Sup. 29 (1996) 483-517. | Numdam | MR | Zbl

[7] Benedicks M., Carleson L., The dynamics of the Hénon map, Ann. of Math. 133 (1991) 73-169. | MR | Zbl

[8] Benedicks M., Viana M., Solution of the basin problem for Hénon-like attractors, Invent. Math. 143 (2001) 375-434. | MR | Zbl

[9] Benedicks M., Young L.-S., Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Ergodic Theory Dynam. Systems 12 (1992) 13-37. | MR | Zbl

[10] Benedicks M., Young L.-S., SBR-measures for certain Hénon maps, Invent. Math. 112 (1993) 541-576. | MR | Zbl

[11] Benedicks M., Young L.-S., Markov extensions and decay of correlations for certain Hénon maps, Astérisque 261 (2000) 13-56. | Numdam | MR | Zbl

[12] P. Collet, Ergodic properties of some unimodal mappings of the interval, Technical report, Institute Mittag-Leffler, 1984.

[13] De Melo W., Van Strien S., One-Dimensional Dynamics, Springer-Verlag, 1993. | MR | Zbl

[14] Díaz L.J., Rocha J., Viana M., Strange attractors in saddle-node cycles: prevalence and globality, Invent. Math. 125 (1996) 37-74. | MR | Zbl

[15] Hayashi S., Connecting invariant manifolds and the solution of the C 1 stability and Ω-stability conjectures for flows, Ann. of Math. 145 (1997) 81-137. | Zbl

[16] Katok A., Kifer Yu., Random perturbations of transformations of an interval, J. Anal. Math. 47 (1986) 193-237. | MR | Zbl

[17] Keller G., Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982) 313-333. | MR | Zbl

[18] Kifer Yu., Ergodic Theory of Random Perturbations, Birkhäuser, 1986. | MR

[19] Kifer Yu., Random Perturbations of Dynamical Systems, Birkhäuser, 1988. | MR | Zbl

[20] Mañé R., A proof of the C 1 stability conjecture, Publ. Math. I.H.E.S. 66 (1988) 161-210. | Numdam | MR | Zbl

[21] Metzger R., Stochastic stability for contracting Lorenz maps, Comm. Math. Phys. 212 (2000) 277-296. | MR | Zbl

[22] Mora L., Viana M., Abundance of strange attractors, Acta Math. 171 (1993) 1-71. | MR | Zbl

[23] Palis J., Smale S., Structural stability theorems, in: Global Analysis, Berkeley, 1968, Proc. Sympos. Pure Math., vol. XIV, Amer. Math. Soc., 1970, pp. 223-232. | MR | Zbl

[24] Palis J., Takens F., Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Cambridge University Press, 1993. | MR | Zbl

[25] Pesin Ya., Families of invariant manifolds corresponding to non-zero characteristic exponents, Math. USSR Izv. 10 (1976) 1261-1302. | Zbl

[26] Pugh C., Shub M., Ergodic attractors, Trans. Amer. Math. Soc. 312 (1989) 1-54. | MR | Zbl

[27] Robbin J., A structural stability theorem, Ann. of Math. 94 (1971) 447-493. | MR | Zbl

[28] Robinson C., Structural stability of vector fields, Ann. of Math. 99 (1974) 154-175, Errata, Ann. of Math. 101 (1975) 368. | MR | Zbl

[29] Rokhlin V.A., On the fundamental ideas of measure theory, Amer. Math. Soc. Transl. 10 (1962) 1-52, Transl. from, Mat. Sb. 25 (1949) 107-150. | MR | Zbl

[30] Rudin W., Real and Complex Analysis, McGraw-Hill, 1987. | MR | Zbl

[31] Sinai Ya., Gibbs measures in ergodic theory, Russian Math. Surveys 27 (1972) 21-69. | MR | Zbl

[32] Thieullen Ph., Tresser C., Young L.-S., Positive Lyapunov exponent for generic one-parameter families of unimodal maps, J. Anal. Math. 64 (1994) 121-172. | MR | Zbl

[33] Wang Q., Young L.-S., Strange attractors with one direction of instability, Comm. Math. Phys. 218 (2001) 1-97. | MR | Zbl

[34] Young L.-S., Stochastic stability of hyperbolic attractors, Ergodic Theory Dynam. Systems 6 (1986) 311-319. | MR | Zbl

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