November  2007, 18(4): 829-851. doi: 10.3934/dcds.2007.18.829

Preimage entropy for random dynamical systems

1. 

School of Mathematical Sciences, Peking University, Beijing, 100871, China

Received  March 2006 Revised  February 2007 Published  May 2007

In [6], Cheng and Newhouse introduced and studied the new invariants - preimage entropies for deterministic dynamical systems. In this paper, the analogous notions, measure-theoretic preimage entropy and topological preimage entropy, are formulated for random dynamical systems. Analogues of many known results for entropies, such as the Shannon-McMillan-Breiman Theorem, the Kolmogorov-Sinai Theorem, the Abromov-Rokhlin formula and the power rule, are obtained for preimage entropies. In particular, a variational principle is given.
Citation: Yujun Zhu. Preimage entropy for random dynamical systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 829-851. doi: 10.3934/dcds.2007.18.829
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