Strong stochastic stability for non-uniformly expanding maps

• Type: Article in International Scientific Journal
• Date: 2013

Authors

alves, jf (Author) FCUP; vilarinho, h (Author) Other

Journal

Title: Ergodic Theory and Dynamical Systems

Vol. 33

Pages: 647-692

ISSN: 0143-3857

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 14 Citations

Scopus - 16 Citations

Other information

Authenticus ID: P-005-0H7

DOI: 10.1017/s0143385712000077

Abstract (EN): We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in Alves and Araujo [Random perturbations of non-uniformly expanding maps. Asterisque 286 (2003), 25-62], where the stochastic stability in the weak* topology was proved. Here, under slightly weaker assumptions on the random perturbations, we obtain a stronger version of stochastic stability: convergence of the density of the stationary measure to the density of the Sinai-Ruelle-Bowen (SRB) measure of the unperturbed system in the L-1-norm. As an application of our results, we obtain strong stochastic stability for two classes of non-uniformly expanding maps. The first one is an open class of local diffeomorphisms introduced in Alves, Bonatti and Viana [SRB measures for partially hyperbolic systems whose central direction is mostly expanding. Invent. Math. 140 (2000), 351-398] and the second one is the class of Viana maps.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 46