Variational principles for metric mean dimension with potential of level sets

TL;DR

This paper develops variational principles connecting metric mean dimension with potential to entropy measures for systems with the specification property, and applies these to suspension flows.

Contribution

It introduces three variational principles for upper metric mean dimension with potential of level sets, expanding understanding of dynamical systems with specification.

Findings

Established variational principles for metric mean dimension with potential.

Connected metric mean dimension to entropy of partitions and Katok's entropy.

Applied principles to analyze suspension flows.

Abstract

We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical systems exhibiting the specification property. Moreover, we apply our results to study the metric mean dimension of suspension flows.