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<p>This manuscript investigates polynomial entropy for systems with two independent transformations. First, we introduce the notion of polynomial extended topological entropy for two independent maps, and compare this notion with the polynomial entropy given by Marco (Regul Chaotic Dyn 18:623 655, 2013). Subsequently, using Carathéodory-Pesin structure, we develop polynomial extended entropy for subsets, generalizing Marco’s weak polynomial entropy framework (Marco in Regul Chaotic Dyn 18:623 655, 2013). Finally, we prove a variational principle and an inverse variational principle for this polynomial extended entropy.</p>

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Polynomial Extended Entropy for Independent Maps

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • Zhongxuan Yang,
  • Xiaojun Huang

摘要

This manuscript investigates polynomial entropy for systems with two independent transformations. First, we introduce the notion of polynomial extended topological entropy for two independent maps, and compare this notion with the polynomial entropy given by Marco (Regul Chaotic Dyn 18:623 655, 2013). Subsequently, using Carathéodory-Pesin structure, we develop polynomial extended entropy for subsets, generalizing Marco’s weak polynomial entropy framework (Marco in Regul Chaotic Dyn 18:623 655, 2013). Finally, we prove a variational principle and an inverse variational principle for this polynomial extended entropy.