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Topological r-Entropy and Measure Theoretic r-Entropy for Amenable Group Actions

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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 to infinite countably amenable group actions.

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Acknowledgements

The second author was supported by NNSF of China (11901419).

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Yong Ji

  2. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, 215009, Jiangsu, People’s Republic of China

    Cao Zhao

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  1. Yong Ji
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  2. Cao Zhao
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Correspondence to Cao Zhao.

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Ji, Y., Zhao, C. Topological r-Entropy and Measure Theoretic r-Entropy for Amenable Group Actions. J Dyn Control Syst 28, 817–827 (2022). https://doi.org/10.1007/s10883-021-09554-1

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  • DOI: https://doi.org/10.1007/s10883-021-09554-1

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