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Relative Time-Restricted Sensitivity and Entropy

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Abstract

In this paper, we consider relativization of measure-theoretical- restricted sensitivity. For a given topological dynamical system, we define conditional measure-theoretical-restricted asymptotic rate with respect to sensitivity and obtain that it equals to the reciprocal of the Brin–Katok local entropy for almost every point under the conditional measure.

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Acknowledgements

We would like to thank Professor Wen Huang and Leiye Xu for valuable remarks and discussions. We also thank the anonymous referees for their careful reading and useful suggestions that greatly improved the manuscript. X. Zhou (corresponding author) is supported by NNSF of China (11801193) and the Fundamental Research Funds for the Central Universities 2020kfyXJJS036.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Xiaochen Wang

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Xiaomin Zhou

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  1. Xiaochen Wang
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  2. Xiaomin Zhou
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Correspondence to Xiaomin Zhou.

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Wang, X., Zhou, X. Relative Time-Restricted Sensitivity and Entropy. Commun. Math. Stat. 12, 265–277 (2024). https://doi.org/10.1007/s40304-022-00289-4

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  • DOI: https://doi.org/10.1007/s40304-022-00289-4

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