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Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms

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Abstract

In this paper, local unstable metric entropy, local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. Specially, two variational principles concerning relationships among the above mentioned numbers are formulated.

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Acknowledgement

The author wishes to express his sincere thanks to Professor Yujun Zhu and Professor Weisheng Wu for many useful discussions and constructive suggestions. The author also would like to thank the referees for the detailed review and very valuable suggestions, which led to improvements of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Xinsheng Wang

  2. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China

    Xinsheng Wang

Authors
  1. Xinsheng Wang
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Correspondence to Xinsheng Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11771118, 11801336, 12171400), the Innovation Fund Designated for Graduate Students of Hebei Province (No. CXZZBS2018101), China Scholarship Council (CSC for short) and China Postdoctoral Science Foundation (No. 2021M691889).

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Wang, X. Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms. Chin. Ann. Math. Ser. B 43, 137–160 (2022). https://doi.org/10.1007/s11401-022-0327-4

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  • DOI: https://doi.org/10.1007/s11401-022-0327-4

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