Hausdorff dimension of local level sets of Takagi's function

被引：4
|
作者：
Liu, Chuntai [1 ]
Li, Haixiong [2 ]
机构：
[1] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China
[2] Hubei Univ Educ, Sch Math & Stat, Wuhan 430205, Peoples R China
来源：
MONATSHEFTE FUR MATHEMATIK | 2015年 / 177卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Hausdorff dimension; Catalan numbers; local level sets; Moran set; symbolic space;
D O I：
10.1007/s00605-015-0743-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Takagi's function is a continuous nowhere-differentiable function constructed by Takagi in 1903. In this paper, we study the local level sets of Takagi's function. By using the tools of Moran sets and symbolic spaces, we establish the Hausdorff dimension of local level sets for and obtain the range of the Hausdorff dimension. In addition, we derive a lower bound for the Hausdorff dimension of the set of points whose local level set has Hausdorff dimension s.
引用
收藏
页码：101 / 117
页数：17
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