@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}, mrnumber = {2259614}, zbl = {1131.37033}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.013/} }
TY - JOUR AU - Benedicks, Michael AU - Viana, Marcelo TI - Random perturbations and statistical properties of Hénon-like maps JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 713 EP - 752 VL - 23 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.013/ DO - 10.1016/j.anihpc.2004.10.013 LA - en ID - AIHPC_2006__23_5_713_0 ER -
%0 Journal Article %A Benedicks, Michael %A Viana, Marcelo %T Random perturbations and statistical properties of Hénon-like maps %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 713-752 %V 23 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2004.10.013/ %R 10.1016/j.anihpc.2004.10.013 %G en %F AIHPC_2006__23_5_713_0
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://www.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] Systèmes grossiers, Dokl. Akad. Nauk USSR 14 (1937) 247-251. | Zbl
, ,[3] Attractors and time averages for random maps, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 307-369. | Numdam | MR | Zbl
,[4] 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] Strong stochastic stability and rate of mixing for unimodal maps, Ann. Sci. École Norm. Sup. 29 (1996) 483-517. | Numdam | MR | Zbl
, ,[7] The dynamics of the Hénon map, Ann. of Math. 133 (1991) 73-169. | MR | Zbl
, ,[8] Solution of the basin problem for Hénon-like attractors, Invent. Math. 143 (2001) 375-434. | MR | Zbl
, ,[9] Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Ergodic Theory Dynam. Systems 12 (1992) 13-37. | MR | Zbl
, ,[10] SBR-measures for certain Hénon maps, Invent. Math. 112 (1993) 541-576. | MR | Zbl
, ,[11] 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] One-Dimensional Dynamics, Springer-Verlag, 1993. | MR | Zbl
, ,[14] Strange attractors in saddle-node cycles: prevalence and globality, Invent. Math. 125 (1996) 37-74. | MR | Zbl
, , ,[15] Connecting invariant manifolds and the solution of the stability and Ω-stability conjectures for flows, Ann. of Math. 145 (1997) 81-137. | Zbl
,[16] Random perturbations of transformations of an interval, J. Anal. Math. 47 (1986) 193-237. | MR | Zbl
, ,[17] Stochastic stability in some chaotic dynamical systems, Monatsh. Math. 94 (1982) 313-333. | MR | Zbl
,[18] Ergodic Theory of Random Perturbations, Birkhäuser, 1986. | MR
,[19] Random Perturbations of Dynamical Systems, Birkhäuser, 1988. | MR | Zbl
,[20] A proof of the stability conjecture, Publ. Math. I.H.E.S. 66 (1988) 161-210. | Numdam | MR | Zbl
,[21] Stochastic stability for contracting Lorenz maps, Comm. Math. Phys. 212 (2000) 277-296. | MR | Zbl
,[22] Abundance of strange attractors, Acta Math. 171 (1993) 1-71. | MR | Zbl
, ,[23] Structural stability theorems, in: Global Analysis, Berkeley, 1968, Proc. Sympos. Pure Math., vol. XIV, Amer. Math. Soc., 1970, pp. 223-232. | MR | Zbl
, ,[24] Hyperbolicity and Sensitive-Chaotic Dynamics at Homoclinic Bifurcations, Cambridge University Press, 1993. | MR | Zbl
, ,[25] Families of invariant manifolds corresponding to non-zero characteristic exponents, Math. USSR Izv. 10 (1976) 1261-1302. | Zbl
,[26] Ergodic attractors, Trans. Amer. Math. Soc. 312 (1989) 1-54. | MR | Zbl
, ,[27] A structural stability theorem, Ann. of Math. 94 (1971) 447-493. | MR | Zbl
,[28] Structural stability of vector fields, Ann. of Math. 99 (1974) 154-175, Errata, Ann. of Math. 101 (1975) 368. | MR | Zbl
,[29] 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] Real and Complex Analysis, McGraw-Hill, 1987. | MR | Zbl
,[31] Gibbs measures in ergodic theory, Russian Math. Surveys 27 (1972) 21-69. | MR | Zbl
,[32] Positive Lyapunov exponent for generic one-parameter families of unimodal maps, J. Anal. Math. 64 (1994) 121-172. | MR | Zbl
, , ,[33] Strange attractors with one direction of instability, Comm. Math. Phys. 218 (2001) 1-97. | MR | Zbl
, ,[34] Stochastic stability of hyperbolic attractors, Ergodic Theory Dynam. Systems 6 (1986) 311-319. | MR | Zbl
,Cité par Sources :