Work

On the dimension theory of Okamoto’s function

Year: 2025

Type: article

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 parameter, this value is attained for Lebesgue almost every level set.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.10094

Authors: Rudolf Dániel Prokaj, Balázs Bárány

Institutions: University of North Texas, Budapest University of Technology and Economics

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: University of Cambridge, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal