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Sub-additive Unstable Topological Pressure of Diffeomorphisms

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Abstract

In this paper, we study unstable topological pressure for C1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. Moreover, without any additional assumption, we have established the expected variational principle which connects this unstable topological pressure and the unstable measure theoretic entropy, as well as the corresponding Lyapunov exponent.

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Acknowledgements

We appreciate the referee sincerely for his/her patience, as well as all comments and suggestions, especially the simplified proof of Step 2 for Theorem 1.1.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, China

    Wen Da Zhang

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Zhi Qiang Li & Yun Hua Zhou

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  1. Wen Da Zhang
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  2. Zhi Qiang Li
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  3. Yun Hua Zhou
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Correspondence to Zhi Qiang Li.

Additional information

The first author is supported by NSFC (Grant No. 11501066) and Department of Education in Chongqing City (Grant Nos. KJQN201900724 and KJQN202100722); the second author is supported by Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX1042), as well as Chongqing Key Laboratory of Analytic Mathematics and Applications in Chongqing University; the third author is supported by NSFC (Grant Nos. 11871120 and 11671093)

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Zhang, W.D., Li, Z.Q. & Zhou, Y.H. Sub-additive Unstable Topological Pressure of Diffeomorphisms. Acta. Math. Sin.-English Ser. 38, 2285–2298 (2022). https://doi.org/10.1007/s10114-022-0492-0

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  • DOI: https://doi.org/10.1007/s10114-022-0492-0

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