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Pré-Publication, Document De Travail Année : 2022

APPLICATION OF WAIST INEQUALITY TO ENTROPY AND MEAN DIMENSION

Masaki Tsukamoto
  • Fonction : Auteur

Résumé

Waist inequality is a fundamental inequality in geometry and topology. We apply it to the study of entropy and mean dimension of dynamical systems. We consider equivariant continuous maps π : (X, T) → (Y, S) between dynamical systems and assume that the mean dimension of the domain (X, T) is larger than the mean dimension of the target (Y, S). We exhibit several situations for which the maps π necessarily have positive conditional metric mean dimension. This study has interesting consequences to the theory of topological conditional entropy. In particular it sheds new light on a celebrated result of Lindenstrauss and Weiss about minimal dynamical systems nonembeddable in [0, 1] Z .
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Dates et versions

hal-03907077 , version 1 (19-12-2022)

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  • HAL Id : hal-03907077 , version 1

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Ruxi Shi, Masaki Tsukamoto. APPLICATION OF WAIST INEQUALITY TO ENTROPY AND MEAN DIMENSION. 2022. ⟨hal-03907077⟩
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