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arXiv · 2310.16461

Variational principles of metric mean dimension for random dynamical systems

Yunping Wang·Ercai Chen·Kexiang Yang
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Abstract

It is well-known that the relativized variational principle established by Bogenschutz and Kifer connects the fiber topological entropy and fiber measure-theoretic entropy. In context of random dynamical systems, metric mean dimension was introduced to characterize infinite fiber entropy systems. We give four types of measure-theoretic $\epsilon$-entropies, called measure-theoretic entropy of partitions decreasing in diameter, Shapira's entropy, Katok's entropy and Brin-Katok local entropy, and establish four variational principles for metric mean dimension.

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Yunping Wang, Ercai Chen, Kexiang Yang. 2023-10-25. Variational principles of metric mean dimension for random dynamical systems. https://doi.org/10.1017/s0013091525100990

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