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<p>In this paper, we prove that the weighted fiber topological entropies, defined by the FK metric and the Bowen metric respectively, are equal in random dynamical systems. Moreover, we establish both a Brin-Katok formula and a Katok formula for the weighted FK metric in random dynamical systems.</p>

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Weighted Entropy Formulae on Feldman-Katok Metric of Random Dynamical Systems

  • 期刊论文

  • 发表日期：

    2025年1月23日

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  • Yu Liu,
  • Xiaojun Huang

摘要

In this paper, we prove that the weighted fiber topological entropies, defined by the FK metric and the Bowen metric respectively, are equal in random dynamical systems. Moreover, we establish both a Brin-Katok formula and a Katok formula for the weighted FK metric in random dynamical systems.