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The descriptive set theoretic properties of multifractal topological entropy and its applications

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  • Wang, Tingting
  • Selmi, Bilel
  • Li, Zhiming

Abstract

In this paper, we consider definitions including (q,ϑ)-Bowen topological entropy and (q,ϑ)-packing topological entropy. We systematically explore their properties and measurability and analyze the relationship between (q,ϑ)-packing topological entropy and topological entropy on level sets. Furthermore, the study demonstrates that the domain of (q,ϑ)-packing topological entropy encompasses the domain of the multifractal spectrum of local entropies, providing new perspectives and tools for dynamical systems.

Suggested Citation

  • Wang, Tingting & Selmi, Bilel & Li, Zhiming, 2025. "The descriptive set theoretic properties of multifractal topological entropy and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p3:s0960077925010719
    DOI: 10.1016/j.chaos.2025.117058
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    References listed on IDEAS

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    1. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Guo, Lixin & Selmi, Bilel & Li, Zhiming & Zyoudi, Haythem, 2025. "Probabilistic spaces and generalized dimensions: A multifractal approach," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
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