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arXiv · 2502.20906

Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory

Tingting Wang·Bilel Selmi·Zhiming Li
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Abstract

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

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Tingting Wang, Bilel Selmi, Zhiming Li. 2025-02-28. Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory. https://arxiv.org/abs/2502.20906

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