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<p>In 2025, Cheng introduced the notion of extended receptive entropy for two independent actions, generalizing the receptive topological entropy developed in Ghys&#xa0;et&#xa0;al. [Acta Math. 160(1-2), 105–142 (1988)] and Biś&#xa0;et&#xa0;al. [Qual. Theory Dyn. Syst. 20(2), paper no. 50 (2011)]. We define the extended Pesin receptive entropy of subsets defined by the Carathéodory–Pesin structure for two independent actions, and compare it with Cheng’s extended receptive entropy. We further establish a variational principle and an inverse variational principle for extended Pesin receptive entropy of subsets. Finally, we prove a Billingsley type theorem for extended Pesin receptive entropy.</p>

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Some notes on extended receptive entropy for independent actions

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Zhongxuan Yang,
  • Xiaojun Huang

摘要

In 2025, Cheng introduced the notion of extended receptive entropy for two independent actions, generalizing the receptive topological entropy developed in Ghys et al. [Acta Math. 160(1-2), 105–142 (1988)] and Biś et al. [Qual. Theory Dyn. Syst. 20(2), paper no. 50 (2011)]. We define the extended Pesin receptive entropy of subsets defined by the Carathéodory–Pesin structure for two independent actions, and compare it with Cheng’s extended receptive entropy. We further establish a variational principle and an inverse variational principle for extended Pesin receptive entropy of subsets. Finally, we prove a Billingsley type theorem for extended Pesin receptive entropy.