Variational formula related to the self-affine Sierpinski carpets

Yongxin Gui; Wenxia Li; Dongmei Xiao

doi:10.1002/mana.201400210

Variational formula related to the self-affine Sierpinski carpets

Yongxin Gui, Wenxia Li, Dongmei Xiao

School of Mathematical Sciences

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

Abstract

We consider those subsets of the self-affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.

Original language	English
Pages (from-to)	593-603
Number of pages	11
Journal	Mathematische Nachrichten
Volume	288
Issue number	5-6
DOIs	https://doi.org/10.1002/mana.201400210
State	Published - 1 Apr 2015

Keywords

Digit frequency
Group frequency
Hausdorff dimension
Self-affine Sierpinski carpet

Access to Document

10.1002/mana.201400210

Cite this

@article{e3a35a45b9fa4959a3ce4bc2673489da,

title = "Variational formula related to the self-affine Sierpinski carpets",

abstract = "We consider those subsets of the self-affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.",

keywords = "Digit frequency, Group frequency, Hausdorff dimension, Self-affine Sierpinski carpet",

author = "Yongxin Gui and Wenxia Li and Dongmei Xiao",

note = "Publisher Copyright: {\textcopyright} 2014 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim.",

year = "2015",

month = apr,

day = "1",

doi = "10.1002/mana.201400210",

language = "英语",

volume = "288",

pages = "593--603",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-VCH Verlag",

number = "5-6",

}

TY - JOUR

T1 - Variational formula related to the self-affine Sierpinski carpets

AU - Gui, Yongxin

AU - Li, Wenxia

AU - Xiao, Dongmei

PY - 2015/4/1

Y1 - 2015/4/1

N2 - We consider those subsets of the self-affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.

AB - We consider those subsets of the self-affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.

KW - Digit frequency

KW - Group frequency

KW - Hausdorff dimension

KW - Self-affine Sierpinski carpet

UR - https://www.scopus.com/pages/publications/84927594240

U2 - 10.1002/mana.201400210

DO - 10.1002/mana.201400210

M3 - 文章

AN - SCOPUS:84927594240

SN - 0025-584X

VL - 288

SP - 593

EP - 603

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 5-6

ER -

Variational formula related to the self-affine Sierpinski carpets

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this