Bowen entropy for actions of amenable groups

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• 作者：Dongmei Zheng ; Ercai Chen
• 刊名：Israel Journal of Mathematics
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：212
• 期：2
• 页码：895-911
• 全文大小：200 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511
• 卷排序：212

文摘

Bowen introduced a definition of topological entropy of subset inspired by Hausdorff dimension in 1973 [1]. In this paper we consider the Bowen entropy for amenable group action dynamical systems and show that, under the tempered condition, the Bowen entropy of the whole compact space for a given Følner sequence equals the topological entropy. For the proof of this result, we establish a variational principle related to the Bowen entropy and the Brin–Katok local entropy formula for dynamical systems with amenable group actions.