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<p>In this manuscript, we utilize <i>g</i>-blowup functions to delve into the examination of rigidity, measure-theoretic entropy, and topological entropy. First, we derive an equivalence statement characterizing the rigidity of a system in terms of <i>g</i>-blowup function. Furthermore, we extend Katok’s entropy formula to encompass the measure-theoretic entropy associated with <i>g</i>-blowup function. Finally, we demonstrate an equivalence between the topological entropy associated with <i>g</i>-blowup function and the classical topological entropy.</p>

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Rigidity and Measure-theoretic Entropy with Respect to g-blowup Function

  • 期刊论文

  • 发表日期：

    2025年4月16日

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  • Zhongxuan Yang,
  • Jiajun Zhang

摘要

In this manuscript, we utilize g-blowup functions to delve into the examination of rigidity, measure-theoretic entropy, and topological entropy. First, we derive an equivalence statement characterizing the rigidity of a system in terms of g-blowup function. Furthermore, we extend Katok’s entropy formula to encompass the measure-theoretic entropy associated with g-blowup function. Finally, we demonstrate an equivalence between the topological entropy associated with g-blowup function and the classical topological entropy.