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<p>To characterize the complexity of a system with zero or infinite entropy, we introduce the notions of scaled topological entropy, scaled packing topological entropy, and scaled measure-theoretic entropy for fixed-point free flows. These concepts describe the rate at which nearby orbits diverge, based on any given scaling sequence. Notably, we derive two variational principles in this context.</p>

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Variational Principle of the Scaled Entropy for Fixed-Point Free Flows

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Zhiming Li,
  • Yongjun Zhang,
  • Bilel Selmi

摘要

To characterize the complexity of a system with zero or infinite entropy, we introduce the notions of scaled topological entropy, scaled packing topological entropy, and scaled measure-theoretic entropy for fixed-point free flows. These concepts describe the rate at which nearby orbits diverge, based on any given scaling sequence. Notably, we derive two variational principles in this context.