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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.10584 |
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| _version_ | 1866914116910710784 |
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| author | Bárány, Balázs Prokaj, R. Dániel |
| author_facet | Bárány, Balázs Prokaj, R. Dániel |
| contents | In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set, and we show that for a typical choice of parameters this value is attained for Lebesgue almost every level sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dimension theory of Okamoto's function Bárány, Balázs Prokaj, R. Dániel Dynamical Systems 28A80 (Primary), 37C45 (Secondary) In this paper, we investigate the dimension theory of the one parameter family of Okamoto's function. We compute the Hausdorff, box-counting and Assouad dimensions of the graph for a typical choice of parameter. Furthermore, we study the dimension of the level sets. We give an upper bound on the dimension of every level set, and we show that for a typical choice of parameters this value is attained for Lebesgue almost every level sets. |
| title | On the dimension theory of Okamoto's function |
| topic | Dynamical Systems 28A80 (Primary), 37C45 (Secondary) |
| url | https://arxiv.org/abs/2501.10584 |