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Weighted Entropy Formulae on Feldman-Katok Metric

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Abstract

In this paper, we prove that the weighted topological entropy defined by FK metric and Bowen metric are equal. Moreover, we establish a Brin-Katok formula and a Katok formula on weighted FK metric, respectively.

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Acknowledgements

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.

Funding

The work was supported by the National Natural Science Foundation of China (Nos.12071222 and 11971236). The work was also funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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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

    Yunxiang Xie, Ercai Chen & Jiao Yang

Authors
  1. Yunxiang Xie
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  2. Ercai Chen
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  3. Jiao Yang
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Contributions

Ercai Chen and Jiao Yang conceived the idea; Yunxiang Xie wrote the main manuscript text. All authors reviewed the manuscript.

Corresponding author

Correspondence to Jiao Yang.

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Xie, Y., Chen, E. & Yang, J. Weighted Entropy Formulae on Feldman-Katok Metric. J Dyn Control Syst (2024). https://doi.org/10.1007/s10883-024-09689-x

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