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<p>In this paper, we primarily examine the role of a factor map between two topological dynamical systems under <i>G</i>-action in the context of topological entropy. Firstly, we introduce the definitions of entropy generalisation of a fiber with respect to Bowen topological entropy (upper capacity topological entropy and packing topological entropy, respectively) under amenable group actions. This concept quantifies the ’infinitesimal variation’ in the dynamics relative to its neighboring fibers, yielding an upper semicontinuous fiber entropy function. Subsequently, we prove that the Bowen topological entropy (upper capacity topological entropy and packing topological entropy, respectively) of a compact set is the supremum of the corresponding generalizations of the fibers.</p>

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Topological Entropy of a Factor Map Under Amenable Group Actions

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Zhongxuan Yang,
  • Xiaojun Huang,
  • Yu Liu

摘要

In this paper, we primarily examine the role of a factor map between two topological dynamical systems under G-action in the context of topological entropy. Firstly, we introduce the definitions of entropy generalisation of a fiber with respect to Bowen topological entropy (upper capacity topological entropy and packing topological entropy, respectively) under amenable group actions. This concept quantifies the ’infinitesimal variation’ in the dynamics relative to its neighboring fibers, yielding an upper semicontinuous fiber entropy function. Subsequently, we prove that the Bowen topological entropy (upper capacity topological entropy and packing topological entropy, respectively) of a compact set is the supremum of the corresponding generalizations of the fibers.