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<p>In this paper we study topological entropy dimension on an arbitrary subset and give the definitions of Bowen topological entropy dimension and packing topological entropy dimension for amenable group actions. Moreover, we introduce the <i>α</i>-local entropy for any Borel probability measure on a compact metric space, and investigate the relation between <i>α</i>-local entropy of Borel probability measures and Bowen <i>α</i>-topological entropy. Also, we establish a variational principle for packing topological entropy dimension on compact subsets in the context of amenable group actions.</p>

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Topological Entropy Dimension of Amenable Group Actions for Noncompact Sets

  • 期刊论文

  • 发表日期：

    2025年1月5日

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  • Lei Liu,
  • Jinlei Jiao,
  • Xiaoyao Zhou

摘要

In this paper we study topological entropy dimension on an arbitrary subset and give the definitions of Bowen topological entropy dimension and packing topological entropy dimension for amenable group actions. Moreover, we introduce the α-local entropy for any Borel probability measure on a compact metric space, and investigate the relation between α-local entropy of Borel probability measures and Bowen α-topological entropy. Also, we establish a variational principle for packing topological entropy dimension on compact subsets in the context of amenable group actions.