Remarks on Metric Entropy of Random \({\mathbb {Z}}^2\) Actions on a Non-compact Space

  • Zhiming LiEmail author
  • Dingxuan Tang


In this paper, we establish Brin–Katok local entropy and Katok \(\delta \) entropy formula of random \({\mathbb {Z}}^2\) transformations on a non-compact space.


Metric entropy Local entropy Random dynamical system 

Mathematics Subject Classification

37A35 37H99 



The first author was supported by National Natural Science Foundation of China (No. 11871394), Israel Science Foundation (No. 1289/17) and Natural Science Foundation of Shaanxi Provincial Department of Education (No. 17JK0755). He would also like to thank Professor Jon Aaronson and the School of mathematical sciences of Tel Aviv University for hospitality during his visit there.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of MathematicsNorthwest UniversityXi’anPeople’s Republic of China

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