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The metric entropy of random dynamical systems in a Banach space: Ruelle inequality

Published online by Cambridge University Press:  15 November 2012

ZHIMING LI  and
LIN SHU
ZHIMING LI
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])
LIN SHU
Affiliation:
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])
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Abstract

Consider a random cocycle Φ on a separable infinite-dimensional Banach space preserving a probability measure, which is supported on a random compact set. We show that if Φ satisfies some mild integrability conditions on the differentials, then Ruelle’s inequality relating entropy and positive Lyapunov exponents holds.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 2 , April 2014 , pp. 594 - 615
Copyright
©2012 Cambridge University Press 

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