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arXiv · 2305.13222

Measure-theoretic Uniformly Positive Entropy on the Space of Probability Measures

Rômulo M. Vermersch
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Abstract

For a homeomorphism $T$ on a compact metric space $X$, a $T$-invariant Borel probability measure $μ$ on $X$ and a measure-theoretic quasifactor $\widetildeμ$ of $μ$, we study the relationship between the local entropy of the system $(X,μ,T)$ and of its induced system $(\mathcal{M}(X),\widetildeμ,\widetilde{T})$, where $\widetilde{T}$ is the homeomorphism induced by $T$ on the space $\mathcal{M}(X)$ of all Borel probability measures defined on $X$.

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Rômulo M. Vermersch. 2023-10-10. Measure-theoretic Uniformly Positive Entropy on the Space of Probability Measures. https://arxiv.org/abs/2305.13222

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