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SRB measures as zero-noise limits

Published online by Cambridge University Press:  19 May 2005

WILLIAM COWIESON  and
LAI-SANG YOUNG
WILLIAM COWIESON
Affiliation:
Courant Institute of Mathematical Science, 251 Mercer Street, New York, NY 10012, USA (e-mail: cowieson@cims.nyu.edu, lsy@cims.nyu.edu)
LAI-SANG YOUNG
Affiliation:
Courant Institute of Mathematical Science, 251 Mercer Street, New York, NY 10012, USA (e-mail: cowieson@cims.nyu.edu, lsy@cims.nyu.edu)
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 4 , August 2005 , pp. 1115 - 1138
Copyright
2005 Cambridge University Press

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