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Deviation property of periodic measures in C 1 non-uniformly hyperbolic systems with limit domination

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Abstract

In a C 1 non-uniformly hyperbolic systems with limit domination, we consider the periodic measures that supported on the Pesin set and keep a distance at least δ to a hyperbolic ergodic measure µ given before. And then, we bound from top the exponential growth rate of such periodic measures by the supremum of measure theoretic entropy on a closed set.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, 100871, P. R. China

    Sheng Qian & Wen Xiang Sun

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Xue Ting Tian

Authors
  1. Sheng Qian
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  2. Wen Xiang Sun
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  3. Xue Ting Tian
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Corresponding author

Correspondence to Sheng Qian.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant No. 10671006); the second author is supported by National Natural Science Foundation of China (Grant Nos. 10671006, 10831003) and National Basic Research Program of China (973 Program, 2006CB805903); the third author is supported by CAPES (Brazil)

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Qian, S., Sun, W.X. & Tian, X.T. Deviation property of periodic measures in C 1 non-uniformly hyperbolic systems with limit domination. Acta. Math. Sin.-English Ser. 28, 1727–1740 (2012). https://doi.org/10.1007/s10114-012-0345-3

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  • DOI: https://doi.org/10.1007/s10114-012-0345-3

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