Subsets of the general sierpinski carpet with mixed group frequencies

Yongxin Gui; Wenxia Li

doi:10.1142/S0129167X09005765

Subsets of the general sierpinski carpet with mixed group frequencies

Yongxin Gui^*, Wenxia Li

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

We consider a class of subsets of the general Sierpinski carpet which is characterized by insisting that the allowed digits in the expansion occur with prescribed mixing group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive and finite.

Original language	English
Pages (from-to)	1289-1303
Number of pages	15
Journal	International Journal of Mathematics
Volume	20
Issue number	10
DOIs	https://doi.org/10.1142/S0129167X09005765
State	Published - Oct 2009

Keywords

Hausdorff dimension
Hausdorff measure
Mixing group frequencies
Sierpinski carpets

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10.1142/S0129167X09005765

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title = "Subsets of the general sierpinski carpet with mixed group frequencies",

abstract = "We consider a class of subsets of the general Sierpinski carpet which is characterized by insisting that the allowed digits in the expansion occur with prescribed mixing group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive and finite.",

keywords = "Hausdorff dimension, Hausdorff measure, Mixing group frequencies, Sierpinski carpets",

author = "Yongxin Gui and Wenxia Li",

year = "2009",

month = oct,

doi = "10.1142/S0129167X09005765",

language = "英语",

volume = "20",

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T1 - Subsets of the general sierpinski carpet with mixed group frequencies

AU - Gui, Yongxin

AU - Li, Wenxia

PY - 2009/10

Y1 - 2009/10

N2 - We consider a class of subsets of the general Sierpinski carpet which is characterized by insisting that the allowed digits in the expansion occur with prescribed mixing group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive and finite.

AB - We consider a class of subsets of the general Sierpinski carpet which is characterized by insisting that the allowed digits in the expansion occur with prescribed mixing group frequencies, determine their Hausdorff dimensions and give the necessary and sufficient conditions for their corresponding Hausdorff measures to be positive and finite.

KW - Hausdorff dimension

KW - Hausdorff measure

KW - Mixing group frequencies

KW - Sierpinski carpets

UR - https://www.scopus.com/pages/publications/70449377906

U2 - 10.1142/S0129167X09005765

DO - 10.1142/S0129167X09005765

M3 - 文章

AN - SCOPUS:70449377906

SN - 0129-167X

VL - 20

SP - 1289

EP - 1303

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 10

ER -

Subsets of the general sierpinski carpet with mixed group frequencies

Abstract

Keywords

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