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Variational Principle for Neutralized Bowen Topological Entropy

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Abstract

Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as

$$B_n(x,e^{-n\epsilon })=\{y\in X: d(T^jx, T^jy)<e^{-n\epsilon }, \forall 0\le j\le n-1\}.$$

We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin–Katok local entropy and neutralized Katok’s entropy.

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Acknowledgements

We would like to thank the anonymous referees for abundant valuable comments that greatly improved the previous manuscript. The first author is supported by Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX23_1665). The second author is supported by the National Natural Science Foundation of China (No.12071222). The third author is supported by the National Natural Science Foundation of China (No. 11971236). The work was also funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. We would like to express our gratitude to Tianyuan Mathematical Center in Southwest China(No.11826102), Sichuan University and Southwest Jiaotong University for their support and hospitality.

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Authors and Affiliations

  1. School of Mathematical Sciences and Institute of Mathematics, Ministry of Education Key Laboratory of NSLSCS, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Rui Yang, Ercai Chen & Xiaoyao Zhou

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  1. Rui Yang
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  2. Ercai Chen
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  3. Xiaoyao Zhou
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Rui Yang, Ercai Chen and Xiaoyao Zhou have contributed equally to the work.

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Correspondence to Xiaoyao Zhou.

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Yang, R., Chen, E. & Zhou, X. Variational Principle for Neutralized Bowen Topological Entropy. Qual. Theory Dyn. Syst. 23, 162 (2024). https://doi.org/10.1007/s12346-024-01029-5

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