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Topological mean dimension of induced systems

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arxiv 2206.10508 v1 pith:JU6WNNXE submitted 2022-06-21 math.DS

David Burguet , Ruxi Shi This is my paper · ORCID
classification math.DS
keywords topologicaldimensionentropyinducedmeandistancedivergenceendowed
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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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  1. Local entropy theory, combinatorics, and local theory of Banach spaces

    math.DS 2025-07 accept novelty 8.0 of 10

    For amenable group actions, IE-tuples of the induced measure system equal the closed convex hull of IE-tuples of the original system, with partial analogues for IN and IT tuples and a sharp n ≤ C log m embedding bound...

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