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Local unstable entropy and local unstable pressure for random partially hyperbolic dynamical systems

  • * Corresponding author: Weisheng Wu

    * Corresponding author: Weisheng Wu 

X. Wang and Y. Zhu are supported by NSFC (Nos: 11771118, 11801336), W. Wu is supported by NSFC (No: 11701559). The first author is also supported by the Innovation Fund Designated for Graduate Students of Hebei Province (No: CXZZBS2018101) and China Scholarship Council (CSC)

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  • Let $ \mathcal{F} $ be a random partially hyperbolic dynamical system generated by random compositions of a set of $ C^2 $-diffeomorphisms. For the unstable foliation, the corresponding local unstable measure-theoretic entropy, local unstable topological entropy and local unstable pressure via the dynamics of $ \mathcal{F} $ along the unstable foliation are introduced and investigated. And variational principles for local unstable entropy and local unstable pressure are obtained respectively.

    Mathematics Subject Classification: Primary: 37D30, 37D35; Secondary: 37H99.


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