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arXiv · 2407.16548

Variational principles for metric mean dimension with potential of level sets

Lucas Backes·Chunlin Liu·Fagner B. Rodrigues
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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.

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Lucas Backes, Chunlin Liu, Fagner B. Rodrigues. 2024-07-23. Variational principles for metric mean dimension with potential of level sets. https://doi.org/10.1007/s10883-026-09767-2

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