On the dimension theory of Okamoto’s function
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 parameter, this value is attained for Lebesgue almost every level set.
Authors
- Balázs Bárány (ORCID: https://orcid.org/0000-0002-0129-8385)
- Rudolf Dániel Prokaj (ORCID: https://orcid.org/0000-0003-3379-7215)
Institutions
- University of North Texas (US)
- Budapest University of Technology and Economics (HU)
Publication Details
- Journal
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Published
- 2025-11-14
- DOI
- https://doi.org/10.1017/prm.2025.10094
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- University of Cambridge
- Nemzeti Kutatási Fejlesztési és Innovációs Hivatal