Variational principles for Feldman-Katok metric mean dimension

Ercai Chen; Rui Yang; Yunxiang Xie

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Variational principles for Feldman-Katok metric mean dimension

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arxiv 2208.09645 v2 pith:T5JOLXCV submitted 2022-08-20 math.DS

Yunxiang Xie , Ercai Chen , Rui Yang This is my paper · ORCID

classification math.DS

keywords meanmetricdimensionsfeldman-katokentropyepsilonprinciplesvariational

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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.

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