Variational principles for Feldman-Katok metric mean dimension

Yunxiang Xie; Ercai Chen; Rui Yang

Variational principles for Feldman-Katok metric mean dimension

Dynamical Systems 2023-10-11 v2

Authors: Yunxiang Xie , Ercai Chen , Rui Yang

Abstract

We introduce the notion of Feldman-Katok metric mean dimensions in this note. We show metric mean dimensions defined by different metrics coincide under weak tame growth of covering numbers, and establish variational principles for Feldman-Katok metric mean dimensions in terms of FK Katok $\epsilon$ -entropy and FK local $\epsilon$ -entropy function.

Keywords

mean dimension assouad dimension metric spaces

Cite

@article{arxiv.2208.09645,
  title  = {Variational principles for Feldman-Katok metric mean dimension},
  author = {Yunxiang Xie and Ercai Chen and Rui Yang},
  journal= {arXiv preprint arXiv:2208.09645},
  year   = {2023}
}

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12 pages

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