Hausdorff dimension of fiber-coding sub-Sierpinski carpets

Yongxin Gui; Wenxia Li

doi:10.1016/j.jmaa.2006.08.071

Hausdorff dimension of fiber-coding sub-Sierpinski carpets

Yongxin Gui
, Wenxia Li^*

^*Corresponding author for this work

School of Mathematical Sciences

Department of Mathematics
East China Normal University
Hubei University of Science and Technology
Department of Mathematics

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

10 Scopus citations

Abstract

In this paper we study a class of subset of Sierpinski carpets for which the allowed digits in the expansions fall into each fiber set with a prescribed frequency. We calculate the Hausdorff and packing dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff and packing measures to be finite.

Original language	English
Pages (from-to)	62-68
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	331
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2006.08.071
State	Published - 1 Jul 2007

Keywords

Hausdorff dimension
Hausdorff measure
Packing dimension
Packing measure
Sierpinski carpets

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10.1016/j.jmaa.2006.08.071

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title = "Hausdorff dimension of fiber-coding sub-Sierpinski carpets",

abstract = "In this paper we study a class of subset of Sierpinski carpets for which the allowed digits in the expansions fall into each fiber set with a prescribed frequency. We calculate the Hausdorff and packing dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff and packing measures to be finite.",

keywords = "Hausdorff dimension, Hausdorff measure, Packing dimension, Packing measure, Sierpinski carpets",

author = "Yongxin Gui and Wenxia Li",

year = "2007",

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doi = "10.1016/j.jmaa.2006.08.071",

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AU - Gui, Yongxin

AU - Li, Wenxia

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Y1 - 2007/7/1

N2 - In this paper we study a class of subset of Sierpinski carpets for which the allowed digits in the expansions fall into each fiber set with a prescribed frequency. We calculate the Hausdorff and packing dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff and packing measures to be finite.

AB - In this paper we study a class of subset of Sierpinski carpets for which the allowed digits in the expansions fall into each fiber set with a prescribed frequency. We calculate the Hausdorff and packing dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff and packing measures to be finite.

KW - Hausdorff dimension

KW - Hausdorff measure

KW - Packing dimension

KW - Packing measure

KW - Sierpinski carpets

UR - https://www.scopus.com/pages/publications/33947113314

U2 - 10.1016/j.jmaa.2006.08.071

DO - 10.1016/j.jmaa.2006.08.071

M3 - 文章

AN - SCOPUS:33947113314

SN - 0022-247X

VL - 331

SP - 62

EP - 68

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Hausdorff dimension of fiber-coding sub-Sierpinski carpets

Abstract

Keywords

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