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arXiv · 2206.10508

Topological mean dimension of induced systems

David Burguet·Ruxi Shi
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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. 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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David Burguet, Ruxi Shi. 2022-06-21. Topological mean dimension of induced systems. https://arxiv.org/abs/2206.10508

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