Hausdorff dimension of local level sets of Takagi’s function

Autor:	Haixiong Li, Chuntai Liu
Rok vydání:	2015
Předmět:	Discrete mathematics Hausdorff distance Packing dimension General Mathematics Hausdorff dimension Minkowski–Bouligand dimension Mathematics::General Topology Dimension function Hausdorff measure Urysohn and completely Hausdorff spaces Effective dimension Mathematics
Zdroj:	Monatshefte für Mathematik. 177:101-117
ISSN:	1436-5081 0026-9255
DOI:	10.1007/s00605-015-0743-6
Popis:	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 $$x\in [0,1]$$ and obtain the range of the Hausdorff dimension. In addition, we derive a lower bound for the Hausdorff dimension of the set of points $$x$$ whose local level set has Hausdorff dimension $$s$$ .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d3f198962ebc756e9ec3ecefe6a5d8a9 https://doi.org/10.1007/s00605-015-0743-6 Zobrazit plný text záznamu Full text from SpringerLink