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Journal of Dynamics and Differential Equations

, Volume 30, Issue 3, pp 937–955 | Cite as

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

  • Cao Zhao
  • Ercai Chen
  • Xiaoyao Zhou
  • Zheng Yin
Article
  • 92 Downloads

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.

Keywords

Weighted entropy Generic points Variational principle 

Mathematics Subject Classification

37D35 

Notes

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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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Cao Zhao
    • 1
  • Ercai Chen
    • 1
    • 2
  • Xiaoyao Zhou
    • 1
  • Zheng Yin
    • 3
  1. 1.School of Mathematical ScienceNanjing Normal UniversityNanjingPeople’s Republic of China
  2. 2.Center of Nonlinear ScienceNanjing UniversityNanjingPeople’s Republic of China
  3. 3.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouPeople’s Republic of China

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