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Application of waist inequality to entropy and mean dimension: II

Volume 267 / 2024

Masaki Tsukamoto Fundamenta Mathematicae 267 (2024), 87-98 MSC: Primary 37B99; Secondary 54F45 DOI: 10.4064/fm231221-28-3 Published online: 15 July 2024

Abstract

Let $X$ be the full-shift on the alphabet $[0, 1]^a$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that every equivariant continuous map from $X$ to $Y$ has conditional metric mean dimension at least $a-{\rm mdim}(Y, S)$. This solves a problem posed in part I of this paper (2023), co-authored with Ruxi Shi.

Authors

  • Masaki TsukamotoDepartment of Mathematics
    Kyoto University
    Kyoto 606-8502, Japan
    e-mail

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