Variational principles for metric mean dimension with potential of level sets

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.

References in corpus (5)

• A variational principle for topological pressure for certain non-compact sets
• The thermodynamic approach to multifractal analysis
• Bowen's equations for upper metric mean dimension with potential
• A variational principle for the metric mean dimension of level sets
• The irregular set for maps with almost weak specification property has full metric mean dimension