Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913712680468480 |
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| author | Wang, Tingting Selmi, Bilel Li, Zhiming |
| author_facet | Wang, Tingting Selmi, Bilel Li, Zhiming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory Wang, Tingting Selmi, Bilel Li, Zhiming Dynamical Systems 37D35 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. |
| title | Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory |
| topic | Dynamical Systems 37D35 |
| url | https://arxiv.org/abs/2502.20906 |