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<p>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 for dynamical systems exhibiting the specification property. Moreover, we apply our results to investigate the metric mean dimension of suspension flows. As a byproduct, we establish certain properties of suspension flows and prove a measure-theoretic metric mean dimension version of Abramov’s formula.</p>

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Variational Principles for Metric Mean Dimension with Potential of Level Sets

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Lucas Backes,
  • Chunlin Liu,
  • Fagner B. Rodrigues

摘要

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 for dynamical systems exhibiting the specification property. Moreover, we apply our results to investigate the metric mean dimension of suspension flows. As a byproduct, we establish certain properties of suspension flows and prove a measure-theoretic metric mean dimension version of Abramov’s formula.