On the dimension theory of Okamoto's function

2025/01/17 by Balázs Bárány, Bárány, Balázs, R. D. Prokaj +1 · 1 citation
Mathematics · #advanced mathematical theories #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2501.10584

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.

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• The higher order partial derivatives of Okamoto's function with respect to the parameter

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