On the dimension theory of Okamoto's function
Dynamical Systems
2025-10-29 v2
Abstract
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.
Cite
@article{arxiv.2501.10584,
title = {On the dimension theory of Okamoto's function},
author = {Balázs Bárány and R. Dániel Prokaj},
journal= {arXiv preprint arXiv:2501.10584},
year = {2025}
}