Variational principles of metric mean dimension for random dynamical systems

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.

References in corpus (1)

• Bowen's equations for upper metric mean dimension with potential