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Multifractal analysis of the historic set in non-uniformly hyperbolic systems

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Abstract

We get the exact Hausdorff dimension of the historic set for ratios of the Birkhoff average in a class of one dimensional non-uniformly hyperbolic dynamical systems.

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Acknowledgements

The authors are grateful to Prof. Zhiying Wen, Prof. Pierre Arnoux, Prof. Fan Aihua for their discussion during the preparation of this paper. They also thank the anonymous referee for his or her helpful comments and suggestions that improved the manuscript. The research work of Guan-zhong Ma was supported by the Key Project of Natural Science Foundation of Educational Committee of Henan Province (Grant No. 15A110005). The research work of Xiao Yao was supported by NSFC No.11271215.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, Henan, China

    Guan-zhong Ma

  2. Shanghai center for mathematical sciences, Fudan University, Shanghai, 200433, China

    Xiao Yao

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  1. Guan-zhong Ma
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  2. Xiao Yao
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Correspondence to Guan-zhong Ma.

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Ma, Gz., Yao, X. Multifractal analysis of the historic set in non-uniformly hyperbolic systems. Arch. Math. 108, 405–413 (2017). https://doi.org/10.1007/s00013-017-1023-6

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  • DOI: https://doi.org/10.1007/s00013-017-1023-6

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