Intersection of Siepinski gasket with its translation

Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS fa(x)=x+aq:a∈{(0,0),(0,1),(1,0)}. In this paper, we provide a description of the following set for 2<q<3Dq={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,...

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Bibliographic Details
Published inIndagationes mathematicae Vol. 31; no. 6; pp. 984 - 996
Main Authors Cai, Yi, Li, Wenxia
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.11.2020
Elsevier Science Ltd
Subjects
Hausdorff dimension
Intersection of Siepinski gasket
Self-similar sets
Self-similarity
Unique expansion
Intersection of Siepinski gasket
Hausdorff dimension
Self-similar sets
Unique expansion
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Summary:Let E be the Sierpinski gasket, i.e., the self-similar set generated by the IFS fa(x)=x+aq:a∈{(0,0),(0,1),(1,0)}. In this paper, we provide a description of the following set for 2<q<3Dq={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.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2020.09.002