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Formula of entropy along unstable foliations for $C^1$ diffeomorphisms with dominated splitting

  • * The corresponding author

    * The corresponding author

It is supported by NSFC(No:11371120,11771118). The third author is also supported by Fundamental Research Funds for the Central University, China(No:20720170004)

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  • Metric entropies along a hierarchy of unstable foliations are investigated for $C^1 $ diffeomorphisms with dominated splitting. The analogues of Ruelle's inequality and Pesin's formula, which relate the metric entropy and Lyapunov exponents in each hierarchy, are given.

    Mathematics Subject Classification: Primary: 37A35, 37D30; Secondary: 37C40.


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