On variational principle for upper metric mean dimension with potential
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.
Cite
@article{arxiv.2207.01901,
title = {On variational principle for upper metric mean dimension with potential},
author = {Rui Yang and Ercai Chen and Xiaoyao Zhou},
journal= {arXiv preprint arXiv:2207.01901},
year = {2024}
}
Comments
Final version. Many typos and mistakes are corrected. The main result was covered by the preprint [arXiv:2210.13126](Theorem 1.1), and was also coverd by Theorem A in [Carvalho, Pessil and Varandas, A convex analysis approach to the metric mean dimension: limits of scaled pressures and variational principles , Adv. Math. (436)(2024), Paper No. 109407, 54 pp.]