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Stochastic stability of diffeomorphisms with dominated splitting | | Jose F. Alves
; Vitor Araujo
; Carlos H. Vasquez
; | | Date: |
7 Apr 2004 | | Subject: | Dynamical Systems MSC-class: 37D25; 37C40; 37H15 | math.DS | | Abstract: | We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic stability of such dynamical systems. We show that a certain $C^2$-open class of nonuniformly hyperbolic diffeomorphisms introduced in [Alves, J; Bonatti, C. and Viana, V., SRB measures for partially hyperbolic systems with mostly expanding central direction, Invent. Math., 140 (2000), 351-398] are stochastically stable. Our setting encompasses that of partially hyperbolic diffeomorphisms as well. Moreover, the techniques used enable us to obtain SRB measures in this setting through zero-noise limit measures. In addition, uniformly hyperbolic diffeomorphisms satisfy our condition and we also obtain their stochastic stability as a corollary. | | Source: | arXiv, math.DS/0404160 | | Services: | Forum | Review | PDF | Favorites | |
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