Hausdorff dimension of subsets with proportional fibre frequencies of the general sierpinski carpet

Yongxin Gui; Wenxia Li

doi:10.1088/0951-7715/20/10/005

Hausdorff dimension of subsets with proportional fibre frequencies of the general sierpinski carpet

Yongxin Gui, Wenxia Li

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we study a class of subsets of the general Sierpinski carpets for which the digits in the expansions lie in two specified horizontal fibres with proportional frequencies. We calculate the Hausdorff dimension of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.

Original language	English
Pages (from-to)	2353-2364
Number of pages	12
Journal	Nonlinearity
Volume	20
Issue number	10
DOIs	https://doi.org/10.1088/0951-7715/20/10/005
State	Published - 2007

Access to Document

10.1088/0951-7715/20/10/005

Cite this

@article{a6de1e79ef414ceaba51df0a626635f3,

title = "Hausdorff dimension of subsets with proportional fibre frequencies of the general sierpinski carpet",

abstract = "In this paper we study a class of subsets of the general Sierpinski carpets for which the digits in the expansions lie in two specified horizontal fibres with proportional frequencies. We calculate the Hausdorff dimension of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.",

author = "Yongxin Gui and Wenxia Li",

year = "2007",

doi = "10.1088/0951-7715/20/10/005",

language = "英语",

volume = "20",

pages = "2353--2364",

journal = "Nonlinearity",

issn = "0951-7715",

publisher = "IOP Publishing Ltd.",

number = "10",

}

TY - JOUR

T1 - Hausdorff dimension of subsets with proportional fibre frequencies of the general sierpinski carpet

AU - Gui, Yongxin

AU - Li, Wenxia

PY - 2007

Y1 - 2007

N2 - In this paper we study a class of subsets of the general Sierpinski carpets for which the digits in the expansions lie in two specified horizontal fibres with proportional frequencies. We calculate the Hausdorff dimension of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.

AB - In this paper we study a class of subsets of the general Sierpinski carpets for which the digits in the expansions lie in two specified horizontal fibres with proportional frequencies. We calculate the Hausdorff dimension of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.

UR - https://www.scopus.com/pages/publications/50249091212

U2 - 10.1088/0951-7715/20/10/005

DO - 10.1088/0951-7715/20/10/005

M3 - 文章

AN - SCOPUS:50249091212

SN - 0951-7715

VL - 20

SP - 2353

EP - 2364

JO - Nonlinearity

JF - Nonlinearity

IS - 10

ER -

Hausdorff dimension of subsets with proportional fibre frequencies of the general sierpinski carpet

Abstract

Access to Document

Other files and links

Fingerprint

Cite this