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Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory

2025/02/28 by Wang, Tingting, Selmi, Bilel, Li, Zhiming
#37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.20906

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 multifractal analysis.

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