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arXiv · 2207.01901

On variational principle for upper metric mean dimension with potential

Rui Yang·Ercai Chen·Xiaoyao Zhou
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Abstract

Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical metric mean dimension of invariant measures. Moreover, the notion of equilibrium state is introduced to characterize these measures that attain the supremum of the variational principle.

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Rui Yang, Ercai Chen, Xiaoyao Zhou. 2022-07-05. On variational principle for upper metric mean dimension with potential. https://arxiv.org/abs/2207.01901

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