TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

David Burguet; Ruxi Shi

doi:10.1090/tran/9407

TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

David Burguet
, Ruxi Shi

Université de Picardie Jules Verne
Fudan University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

2 Citations (Scopus)

Résumé

For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-∗ topology has infinite topological mean dimension. As an application, it answers a question of Kloeckner [J. Topol. Anal. 4 (2012), pp. 203–235]. We also estimate the rate of divergence of the entropy with respect to the Wasserstein distance when the scale goes to zero.

langue originale	Anglais
Pages (de - à)	3085-3103
Nombre de pages	19
journal	Transactions of the American Mathematical Society
Volume	378
Numéro de publication	5
Les DOIs	https://doi.org/10.1090/tran/9407
état	Publié - 1 mai 2025
Modification externe	Oui

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10.1090/tran/9407

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title = "TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS",

abstract = "For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-∗ topology has infinite topological mean dimension. As an application, it answers a question of Kloeckner [J. Topol. Anal. 4 (2012), pp. 203–235]. We also estimate the rate of divergence of the entropy with respect to the Wasserstein distance when the scale goes to zero.",

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AB - For a topological system with positive topological entropy, we show that the induced transformation on the set of probability measures endowed with the weak-∗ topology has infinite topological mean dimension. As an application, it answers a question of Kloeckner [J. Topol. Anal. 4 (2012), pp. 203–235]. We also estimate the rate of divergence of the entropy with respect to the Wasserstein distance when the scale goes to zero.

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TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

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