Dimension of hyperbolic measures of random diffeomorphisms

Liu, Pei-Dong; Xie, Jian-Sheng

doi:10.1090/S0002-9947-06-03933-X

Dimension of hyperbolic measures of random diffeomorphisms
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by Pei-Dong Liu and Jian-Sheng Xie PDF

Trans. Amer. Math. Soc. 358 (2006), 3751-3780 Request permission

Abstract:

We consider dynamics of compositions of stationary random $C^2$ diffeomorphisms. We will prove that the sample measures of an ergodic hyperbolic invariant measure of the system are exact dimensional. This is an extension to random diffeomorphisms of the main result of Barreira, Pesin and Schmeling (1999), which proves the Eckmann-Ruelle dimension conjecture for a deterministic diffeomorphism.

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