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Katok’s Entropy Formula of Unstable Metric Entropy for Partially Hyperbolic Diffeomorphisms

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Abstract

Katok’s entropy formula is an important formula in entropy theory. It plays significant roles in large deviation theories, multifractal analysis, quantitative recurrence and so on. This paper is devoted to establishing Katok’s entropy formula of unstable metric entropy which is the entropy caused by the unstable part of partially hyperbolic systems. We also construct a similar formula which can be used to study the quantitative recurrence in the unstable manifold for partially hyperbolic diffeomorphisms.

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Acknowledgements

The first author was supported by NNSF of China (12101446, 11401581, 11971236). The second author was supported by NNSF of China (11401581). And the third author was supported by NNSF of China (11671208, 11431012). At the end, we would like to express our gratitude to Tianyuan Mathematical Center in Southwest China, Sichuan University and Southwest Jiaotong University for their support and hospitality.

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Authors and Affiliations

  1. College of Mathematical and Physical Sciences, Taizhou University, Taizhou, 225300, Jiangsu, People’s Republic of China

    Ping Huang & Chenwei Wang

  2. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Ercai Chen

  3. Center of Nonlinear Science, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Ercai Chen

Authors
  1. Ping Huang
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  2. Chenwei Wang
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  3. Ercai Chen
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Correspondence to Chenwei Wang.

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Huang, P., Wang, C. & Chen, E. Katok’s Entropy Formula of Unstable Metric Entropy for Partially Hyperbolic Diffeomorphisms. Commun. Math. Stat. (2022). https://doi.org/10.1007/s40304-022-00293-8

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  • DOI: https://doi.org/10.1007/s40304-022-00293-8

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