Abstract
We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure µ. Let D(µω) be its dimension of the sample measure, then we prove a formula relating D(µω) to the entropy and Lyapunov exponents of the random system, where D(µω) is dimHµω, \(\underline {\dim } _B \mu \omega\), or \(\overline {\dim } _B \mu \omega\).
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