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Intermediate topological entropies: Bridging entropy and dimension theories in dynamical systems

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  • Liu, Yu
  • Selmi, Bilel
  • Li, Zhiming

Abstract

Topological entropy and fractal dimension are core concepts integrating dynamical systems and geometric measure theory, with a profound and far-reaching intrinsic connection between them. Based on this connection, this work extends the concept of intermediate dimensions to the field of dynamical systems, and proposes two new types of dynamical invariants: lower and upper θ-intermediate topological entropies. Compared with classical entropy concepts, these new invariants are expected to provide more detailed dynamical information. In addition, this work systematically presents three equivalent definitions of these two entropies, conducts in-depth research on their core properties, and explores key contents including monotonicity, stability, Frostman’s lemma, the mass distribution principle, and the upper product formula, thus providing new perspectives and support for the research on entropy theory of dynamical systems.

Suggested Citation

  • Liu, Yu & Selmi, Bilel & Li, Zhiming, 2026. "Intermediate topological entropies: Bridging entropy and dimension theories in dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 208(P3).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p3:s0960077926004492
    DOI: 10.1016/j.chaos.2026.118308
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