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Preimage entropy for random dynamical systems

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  • 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.
    Mathematics Subject Classification: 37A35, 37H99.


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