A generalized multifractal spectrum of the general Sierpinski carpets

Yongxin Gui; Wenxia Li

doi:10.1016/j.jmaa.2008.07.008

A generalized multifractal spectrum of the general Sierpinski carpets

Yongxin Gui, Wenxia Li

School of Mathematical Sciences

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

7 Scopus citations

Abstract

In this paper we study a class of subsets of the general Sierpinski carpets for which the limiting frequency of a horizontal fibre falls into a prescribed closed interval. We obtain the explicit expression for the Hausdorff dimension of these subsets in terms of the parameters of the construction and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

Original language	English
Pages (from-to)	180-192
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	348
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2008.07.008
State	Published - 1 Dec 2008

Keywords

General Sierpinski carpets
Hausdorff dimension
Hausdorff measure
Horizontal fibre

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10.1016/j.jmaa.2008.07.008

Cite this

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title = "A generalized multifractal spectrum of the general Sierpinski carpets",

abstract = "In this paper we study a class of subsets of the general Sierpinski carpets for which the limiting frequency of a horizontal fibre falls into a prescribed closed interval. We obtain the explicit expression for the Hausdorff dimension of these subsets in terms of the parameters of the construction and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.",

keywords = "General Sierpinski carpets, Hausdorff dimension, Hausdorff measure, Horizontal fibre",

author = "Yongxin Gui and Wenxia Li",

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AU - Li, Wenxia

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N2 - In this paper we study a class of subsets of the general Sierpinski carpets for which the limiting frequency of a horizontal fibre falls into a prescribed closed interval. We obtain the explicit expression for the Hausdorff dimension of these subsets in terms of the parameters of the construction and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

AB - In this paper we study a class of subsets of the general Sierpinski carpets for which the limiting frequency of a horizontal fibre falls into a prescribed closed interval. We obtain the explicit expression for the Hausdorff dimension of these subsets in terms of the parameters of the construction and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive finite.

KW - General Sierpinski carpets

KW - Hausdorff dimension

KW - Hausdorff measure

KW - Horizontal fibre

UR - https://www.scopus.com/pages/publications/50249123885

U2 - 10.1016/j.jmaa.2008.07.008

DO - 10.1016/j.jmaa.2008.07.008

M3 - 文章

AN - SCOPUS:50249123885

SN - 0022-247X

VL - 348

SP - 180

EP - 192

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A generalized multifractal spectrum of the general Sierpinski carpets

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Keywords

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