This paper establishes variational principles for metric mean dimension using entropy measures, linking dynamics and ergodic theory.
In this paper, we establish variational principles for the metric mean dimension of random dynamical systems with infinite topological entropy. This is based on four types of measure-theoretic ϵ -entropies: Kolmogorov-Sinai ϵ -entropy, Shapira’s ϵ -entropy, Katok’s ϵ -entropy and Brin–Katok local ϵ -entropy. The variational principle, as a fundamental theorem, links topological dynamics and ergodic theory.
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Wang et al. (2025) studied this question.
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