Variational principles for Feldman-Katok metric mean dimension

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.

12 pages