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arXiv · 2312.07793

Application of waist inequality to entropy and mean dimension: II

Masaki Tsukamoto
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Abstract

Let $X$ be a full-shift on the alphabet $[0, 1]^a$ and let $(Y, S)$ be an arbitrary dynamical system. We prove that any equivariant continuous map from $X$ to $Y$ has conditional metric mean dimension not less than $a-\mathrm{mdim}(Y, S)$. This solves a problem posed in a paper of Shi--Tsukamoto (2023).

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Masaki Tsukamoto. 2023-12-12. Application of waist inequality to entropy and mean dimension: II. https://arxiv.org/abs/2312.07793

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