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arXiv · 2005.13940

Uniformly Positive Entropy of Induced Transformations

Nilson C. Bernardes Jr.·Udayan B. Darji·Rômulo M. Vermersch
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Abstract

Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does the induced system $(\cM(X),\wt{T})$ on the space of Borel probability measures endowed with the weak$^*$ topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.

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Nilson C. Bernardes Jr., Udayan B. Darji, Rômulo M. Vermersch. 2020-05-28. Uniformly Positive Entropy of Induced Transformations. https://doi.org/10.1017/etds.2020.136

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