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<p>For topological semigroup actions with a regular system, we introduce several invariance entropies and dimensions in both topological and measure-theoretic contexts. We investigate their fundamental properties and establish variational relations among these quantities. Furthermore, we derive a variational principle for the generalized invariance dimensions.</p>

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Invariance entropies and dimensions of topological semigroup actions

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Xiaoxiao Nie

摘要

For topological semigroup actions with a regular system, we introduce several invariance entropies and dimensions in both topological and measure-theoretic contexts. We investigate their fundamental properties and establish variational relations among these quantities. Furthermore, we derive a variational principle for the generalized invariance dimensions.