Topological r-Entropy and Measure Theoretic r-Entropy for Amenable Group Actions
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Dynamical and Control Systems"
DOI: 10.1007/s10883-021-09554-1
Abstract: In this paper, we introduce the concept of measure theoretic r-entropy on a compact metric space in the context of amenable group actions. To be precise, we generalize Katok’s r-entropy formula and Brin-Katok r-entropy formula… read more here.
Keywords: amenable group; group actions; measure theoretic; theoretic entropy ... See more keywords
Katok formula for the induced measure-theoretic entropy
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DOI: 10.1080/14689367.2017.1329402
Abstract: ABSTRACT Entropy is undoubtedly one of the most essential characteristics of dynamical systems. In this article, we define a topological version of the induced measure-theoretic entropy and obtain its Katok entropy formula. We show that… read more here.
Keywords: induced measure; measure theoretic; entropy; formula ... See more keywords
Measure-theoretic equicontinuity and rigidity
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DOI: 10.1088/1361-6544/ab8a67
Abstract: Let $(X,T)$ be a topological dynamical system and $\mu$ be a invariant measure, we show that $(X,\mathcal{B},\mu,T)$ is rigid if and only if there exists some subsequence $A$ of $\mathbb N$ such that $(X,T)$ is… read more here.
Keywords: theoretic equicontinuity; equicontinuity rigidity; measure; measure theoretic ... See more keywords