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Unstable Pressure and Thermodynamic Formalism in Partially Hyperbolic Systems

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Abstract

In this paper we introduce unstable topological pressure of general sets for partially hyperbolic systems using Caratheódory-Pesin construction. In particular, we use the thermodynamic formalism of unstable topological pressure to obtain some estimates on Birkhoff level sets.

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Acknowledgements

The authors would like to thank the referee for valuable suggestions. X. Tian is supported by NSFC No. 12071082 and Natural Science Foundation of Shanghai No. 23ZR1405800. W. Wu is supported by National Key R &D Program of China No. 2022YFA1007800, NSFC No. 12071474 and NSF of Jiangsu BK20200850.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Xueting Tian

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Weisheng Wu

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  1. Xueting Tian
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  2. Weisheng Wu
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Correspondence to Weisheng Wu.

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Tian, X., Wu, W. Unstable Pressure and Thermodynamic Formalism in Partially Hyperbolic Systems. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10282-2

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  • DOI: https://doi.org/10.1007/s10884-023-10282-2

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