TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

David Burguet; Ruxi Shi

doi:10.1090/tran/9407

TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3085-3103
Number of pages	19
Journal	Transactions of the American Mathematical Society
Volume	378
Issue number	5
DOIs	https://doi.org/10.1090/tran/9407
Publication status	Published - 1 May 2025
Externally published	Yes

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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.",

author = "David Burguet and Ruxi Shi",

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AU - Shi, Ruxi

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N2 - 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.

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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DO - 10.1090/tran/9407

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JO - Transactions of the American Mathematical Society

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TOPOLOGICAL MEAN DIMENSION OF INDUCED SYSTEMS

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