Double Variational Principle of Mean Dimension for ${\mathbb {Z}}^{k}$-Actions

Abstract

Lindenstrauss and Tsukamoto in 2019 established double variational principle for mean dimension. In this paper, we focus on developing the mean dimension theory for ${\mathbb {Z}}^k$-actions. Specifically, we establish a double variational principle for mean dimension of ${\mathbb {Z}}^k$-actions for dynamical systems with the marker property.

Keywords

${\mathbb {Z}}^{k}$-action')">${\mathbb {Z}}^{k}$-action / Mean dimension / Rate distortion dimension / Double variational principle / 37A05 / 37B99

Funding

National Natural Science Foundation of China(12201328)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature