The partial derivative of Okamoto's functions with respect to the parameter

2021/10/22 by Nathan Dalaklis, Dalaklis, Nathan, Kiko Kawamura +5 · 1 citation
Mathematics · #26A27 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis #advanced mathematical theories #math.CA #msc:26A27

paper · pdf · doi:10.48550/arxiv.2110.11555

14 pages, 3 figures

openalex publication_date 2021/10/22 · arxiv created 2021/11/17 · arxiv updated 2021/11/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

The differentiability of the one parameter family of Okomoto's functions as functions of x has been analyzed extensively since their introduction in 2005. As an analogue to a similar investigation, in this paper, we consider the partial derivative of Okomoto's functions with respect to the parameter a. We place a significant focus on a = 1/3 to describe the properties of a nowhere differentiable function K(x) for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension 1.

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

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