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<p>As an extension of weighted entropy, the weighted topological sequence entropy and the weighted measure-theoretic sequence entropy are defined. A variational principle of relating the two weighted sequence entropies is established. The weighted maximal pattern entropy is also defined. It is shown that for homeomorphism dynamical systems the weighted maximal pattern entropy is equal to the supremum of the weighted sequence entropies over all strictly increasing sequences in integers both in topological and measure-theoretic settings.</p>

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Weighted Sequence Entropy and Maximal Pattern Entropy

  • 期刊论文

  • 发表日期：

    2025年4月21日

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  • Xiaoxiao Nie,
  • Yu Huang

摘要

As an extension of weighted entropy, the weighted topological sequence entropy and the weighted measure-theoretic sequence entropy are defined. A variational principle of relating the two weighted sequence entropies is established. The weighted maximal pattern entropy is also defined. It is shown that for homeomorphism dynamical systems the weighted maximal pattern entropy is equal to the supremum of the weighted sequence entropies over all strictly increasing sequences in integers both in topological and measure-theoretic settings.