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SRB measures as zero-noise limits. (English) Zbl 1098.37020
Summary: We consider zero-noise limits of random perturbations of dynamical systems and examine, in terms of the continuity of entropy and Lyapunov exponents, circumstances under which these limits are Sinai-Ruelle-Bowen (SRB) measures. The ideas of this general discussion are then applied to specific classes of attractors. We prove, for example, that partially hyperbolic attractors with one-dimensional center subbundles always admit SRB measures.

MSC:
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37D30 Partially hyperbolic systems and dominated splittings
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