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Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems

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Abstract

This article is devoted to the investigation of the weighted topological entropy of generic points of the ergodic measures in dynamical systems. We showed that the weighted topological entropy of generic points of the ergodic measure \(\mu \) is equal to the weighted measure entropy of \(\mu ,\) which generalized the classical result of Bowen (Trans Am Math Soc 184:125–136, 1973). As an application, we also use the result to study the dimension of generic points for a class of skew product expanding maps on high dimensional tori.

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Acknowledgements

The first and second author were supported by NNSF of China (11671208 and 11431012). The third author was supported by NNSF of China (11601235 and 11271191), NSF of the Jiangsu Higher Education Institutions of China (16KJD110003), NSF of Jiangsu Province (BK20161014) and China Postdoctoral Science Foundation (2016M591873).

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Authors and Affiliations

  1. School of Mathematical Science, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Cao Zhao, Ercai Chen & Xiaoyao Zhou

  2. Center of Nonlinear Science, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Ercai Chen

  3. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Zheng Yin

Authors
  1. Cao Zhao
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  2. Ercai Chen
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  3. Xiaoyao Zhou
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  4. Zheng Yin
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Correspondence to Ercai Chen.

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Zhao, C., Chen, E., Zhou, X. et al. Weighted Topological Entropy of the Set of Generic Points in Topological Dynamical Systems. J Dyn Diff Equat 30, 937–955 (2018). https://doi.org/10.1007/s10884-017-9575-5

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  • DOI: https://doi.org/10.1007/s10884-017-9575-5

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