Double variational principle for mean dimensions with sub-additive potentials

TL;DR

This paper introduces a new framework for mean dimensions incorporating sub-additive potentials and establishes a double variational principle, advancing the theoretical understanding of dynamical systems with complex potential functions.

Contribution

It defines mean dimension and mean metric dimension with sub-additive potentials and proves a double variational principle linking these concepts.

Findings

Established a double variational principle for sub-additive potentials.

Defined new mean dimension quantities with sub-additive potentials.

Extended the theoretical framework of mean dimension in dynamical systems.

Abstract

In this paper, we introduce mean dimension quantities with sub-additive potentials. We define mean dimension with sub-additive potentials and mean metric dimension with sub-additive potentials, and establish a double variational principle for sub-additive potentials.