Infinite derivatives of the Takagi-Van der Waerden functions

2019/03/27 by Juan Ferrera, Ferrera, Juan, Javier Gómez Gil +3
Mathematics · #Advanced Topology and Set Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.CA

paper · pdf · doi:10.48550/arxiv.1903.11631

openalex publication_date 2019/03/27 · arxiv created 2019/03/29 · arxiv updated 2019/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we characterize the set of points where the lateral derivatives of the Takagi-Van der Waerden functions are infinite. We also prove that the set of points with infinite derivative has Hausdorff dimension one and Lebesgue measure zero.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

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