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

^*此作品的通讯作者

数学科学学院

Hubei University of Science and Technology
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	180-192
页数	13
期刊	Journal of Mathematical Analysis and Applications
卷	348
期	1
DOI	https://doi.org/10.1016/j.jmaa.2008.07.008
出版状态	已出版 - 1 12月 2008

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10.1016/j.jmaa.2008.07.008

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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.",

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AU - Li, Wenxia

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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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