Variational principles for metric mean dimension with potential of level sets
Dynamical Systems
2026-05-08 v2
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.
Cite
@article{arxiv.2407.16548,
title = {Variational principles for metric mean dimension with potential of level sets},
author = {Lucas Backes and Chunlin Liu and Fagner B. Rodrigues},
journal= {arXiv preprint arXiv:2407.16548},
year = {2026}
}