The Hausdorff dimension of the level sets of Takagi's function

被引：13

作者：

de Amo, E. ^{[1
]}

Bhouri, I. ^{[2
]}

Diaz Carrillo, M. ^{[3
]}

Fernandez-Sanchez, J. ^{[4
]}

机构：

[1] Univ Almeria, Dept Algebra & Anal Matemat, La Canada De San Urbano 04120, Almeria, Spain

[2] Univ Monastir, Dept Matemat, Monastir 5000, Tunisia

[3] Univ Granada, Dept Anal Matemat, E-18071 Granada, Spain

[4] Univ Almeria, Grp Invest Anal Matemat, La Canada De San Urbano 04120, Almeria, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 15期

关键词：

Takagi's function; Level set; Box counting; Hausdorff dimension;

D O I：

10.1016/j.na.2011.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, Maddock (2006) [12] has conjectured that the Hausdorff dimension of each level set of Takagi's function is at most 1/2. We prove this conjecture using the self-affinity of the function of Takagi and the existing relationship between the Hausdorff and box-counting dimensions. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：5081 / 5087

页数：7

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