Topological mean dimension of induced systems

Burguet, David; Shi, Ruxi

doi:10.1090/tran/9407

Topological mean dimension of induced systems
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by David Burguet and Ruxi Shi;

Trans. Amer. Math. Soc. 378 (2025), 3085-3103

DOI: https://doi.org/10.1090/tran/9407

Published electronically: March 4, 2025

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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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Topological mean dimension of induced systems
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Abstract: