, Volume 47, Issue 1, pp 111-150

General random perturbations of hyperbolic and expanding transformations

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Abstract

Small random perturbations of a general form of diffeomorphisms having hyperbolic invariant sets and expanding maps are considered. The convergence of invariant measures of perturbations to the Sinaî-Bowen-Ruelle measure in the case of a hyperbolic attractor and to the smooth invariant measure in the expanding case are proved. The convergence of corresponding entropy characteristics and the approximation of the topological pressure by means of perturbations is considered as well.

Partially supported by N.S.F. Grant MCS82-04024.