Intersection of Siepinski gasket with its translation

Yi Cai; Wenxia Li

doi:10.1016/j.indag.2020.09.002

Intersection of Siepinski gasket with its translation

Yi Cai^*
, Wenxia Li

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

Abstract

Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS [Formula presented]. In this paper, we provide a description of the following set for 2<q<3 D_q={dim_H(E∩(E+t)):t∈T},where T is the set of t=(t₁,t₂) with t∈E−E and t₁,t₂ have unique q-expansions w.r.t −1,0,1.

Original language	English
Pages (from-to)	984-996
Number of pages	13
Journal	Indagationes Mathematicae
Volume	31
Issue number	6
DOIs	https://doi.org/10.1016/j.indag.2020.09.002
State	Published - Nov 2020

Keywords

Hausdorff dimension
Intersection of Siepinski gasket
Self-similar sets
Unique expansion

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10.1016/j.indag.2020.09.002

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title = "Intersection of Siepinski gasket with its translation",

abstract = "Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS [Formula presented]. In this paper, we provide a description of the following set for 2q=\{dimH(E∩(E+t)):t∈T\},where T is the set of t=(t1,t2) with t∈E−E and t1,t2 have unique q-expansions w.r.t −1,0,1.",

keywords = "Hausdorff dimension, Intersection of Siepinski gasket, Self-similar sets, Unique expansion",

author = "Yi Cai and Wenxia Li",

note = "Publisher Copyright: {\textcopyright} 2020 Royal Dutch Mathematical Society (KWG)",

year = "2020",

month = nov,

doi = "10.1016/j.indag.2020.09.002",

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AU - Cai, Yi

AU - Li, Wenxia

PY - 2020/11

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AB - Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS [Formula presented]. In this paper, we provide a description of the following set for 2q={dimH(E∩(E+t)):t∈T},where T is the set of t=(t1,t2) with t∈E−E and t1,t2 have unique q-expansions w.r.t −1,0,1.

KW - Hausdorff dimension

KW - Intersection of Siepinski gasket

KW - Self-similar sets

KW - Unique expansion

UR - https://www.scopus.com/pages/publications/85091207892

U2 - 10.1016/j.indag.2020.09.002

DO - 10.1016/j.indag.2020.09.002

M3 - 文章

AN - SCOPUS:85091207892

SN - 0019-3577

VL - 31

SP - 984

EP - 996

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 6

ER -

Intersection of Siepinski gasket with its translation

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Keywords

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