Random perturbations of nonuniformly expanding maps

Ferreira Alves, José ; Araújo, Vítor

Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 25-62

MR Zbl | 5 citations dans Numdam

@incollection{AST_2003__286__25_0,
     author = {Ferreira Alves, Jos\'e and Ara\'ujo, V{\'\i}tor},
     title = {Random perturbations of nonuniformly expanding maps},
     booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
     editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
     series = {Ast\'erisque},
     pages = {25--62},
     year = {2003},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {286},
     mrnumber = {2052296},
     zbl = {1043.37016},
     language = {en},
     url = {https://www.numdam.org/item/AST_2003__286__25_0/}
}

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%E Yoccoz, Jean-Christophe
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Ferreira Alves, José; Araújo, Vítor. Random perturbations of nonuniformly expanding maps, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 25-62. https://www.numdam.org/item/AST_2003__286__25_0/

Bibliographie
Cité par

[A1] J. F. Alves, $S R B$ measures for non-hyperbolic systems with multidimensional expansion, Ann. Scient. Éc. Norm. Sup., 4e série, 33 (2000), 1-32. | MR | Zbl | EuDML | Numdam | DOI

[ABV] J. F. Alves, C. Bonatti, M. Viana, $S R B$ measures for partially hyperbolic systems with mostly expanding central direction, Invent. Math. 140 (2000), 351-398. | MR | Zbl | DOI

[AV] J. F. Alves, M. Viana, Statistical stability for robust classes of maps with nonuniform expansion, Erg. Th. & Dyn. Sys 22 (2002), 1-32. | MR | Zbl | DOI

[Ar] V. Araújo, Attractors and time averages for random maps, Ann. de l'Inst. H. Poincaré-Anal. non-Lin. 17 (2000), 307-369. | MR | Zbl | EuDML | Numdam | DOI

[BV] V. Baladi, M. Viana, Strong stochastic stability and rate of mixing for unimodal maps, Ann. Scient. Éc. Norm. Sup., 4e série, 29 (1996), 483-517. | MR | Zbl | EuDML | Numdam | DOI

[BC1] M. Benedicks and L. Carleson, On iterations of $1 - a x^{2}$ on $(- 1, 1)$ , Ann. Math. 122 (1985), 1-25. | MR | Zbl

[BC2] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math. 133 (1991), 73-169. | MR | Zbl | DOI

[BY1] M. Benedicks, L.-S. Young, Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps, Erg. Th. & Dyn. Sys. 12 (1992), 13-37. | MR | Zbl | DOI

[BY2] M. Benedicks and L.-S. Young, $S R B$ -measures for certain Hénon maps, Invent. Math. 112 (1993), 541-576. | MR | Zbl | EuDML | DOI

[BV] C. Bonatti and M. Viana, $S R B$ measures for partially hyperbolic systems with mostly contracting central direction, Isr. J. Math. 115 (2000), 157-193. | MR | Zbl | DOI

[BR] R. Bowen and D. Ruelle, The ergodic theory of Axiom $A$ flows, Invent. Math. 29 (1975), 181-202. | MR | Zbl | EuDML | DOI

[HPS] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Lect. Notes in Math. 583, Springer Verlag, 1977. | MR | Zbl

[Ja] M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps, Comm. Math. Phys. 81 (1981), 39-88. | MR | Zbl | DOI

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

[Ki1] Y. Kifer, Ergodic theory of random transformations, Birkhäuser, Boston Basel, 1986. | MR | Zbl | DOI

[Ki2] Y. Kifer, Random perturbations of dynamical systems, Birkhäuser, Boston Basel, 1988. | MR | Zbl | DOI

[Ma] R. Mañé, Ergodic theory and differentiable dynamics, Springer-Verlag, 1987. | MR | Zbl

[Pl] V. Pliss, On a conjecture due to Smale, Diff. Uravnenija, 8 (1972), 262-268. | Zbl | MR

[Ru] D. Ruelle, A measure associated with Axiom $A$ attractors, Amer. Jour. Math. 98 (1976), 619-654. | MR | Zbl | DOI

[Si] Ya. Sinai, Gibbs measures in ergodic theory, Russ. Math. Surv. 27, n. 4, (1972), 21-69. | Zbl | MR | DOI

[Vi1] M. Viana, Multidimensional non-hyperbolic attractors, Publ. Math. IHES 85 (1997), 63-96. | MR | Zbl | EuDML | DOI

[Vi2] M. Viana, Stochastic dynamics of deterministic systems, Lect. Notes XXI Braz. Math Colloq., IMPA, 1997.

[Yo] L.-S. Young, Stochastic stability of hyperbolic attractors, Erg. Th. & Dyn. Sys. 6 (1986), 311-319. | MR | Zbl