Unique expansion of points of a class of self-similar sets with overlaps

Yuru Zou; Jian Lu; Wenxia Li

doi:10.1112/S0025579312000083

Unique expansion of points of a class of self-similar sets with overlaps

Yuru Zou^*
, Jian Lu
, Wenxia Li

^*Corresponding author for this work

School of Mathematical Sciences

Shenzhen University

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

9 Scopus citations

Abstract

For q>1, the set F q of real numbers which can be expanded in base q with respect to the digit set {0,1,q} is just a self-similar set with overlaps. We consider the subset of F _q whose elements have a unique expansion and calculate its Hausdorff dimension for the case where q≫ (3+5)/2.

Original language	English
Pages (from-to)	371-388
Number of pages	18
Journal	Mathematika
Volume	58
Issue number	2
DOIs	https://doi.org/10.1112/S0025579312000083
State	Published - Jul 2012

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title = "Unique expansion of points of a class of self-similar sets with overlaps",

abstract = "For q>1, the set F q of real numbers which can be expanded in base q with respect to the digit set \{0,1,q\} is just a self-similar set with overlaps. We consider the subset of F q whose elements have a unique expansion and calculate its Hausdorff dimension for the case where q≫ (3+5)/2.",

author = "Yuru Zou and Jian Lu and Wenxia Li",

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AU - Lu, Jian

AU - Li, Wenxia

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AB - For q>1, the set F q of real numbers which can be expanded in base q with respect to the digit set {0,1,q} is just a self-similar set with overlaps. We consider the subset of F q whose elements have a unique expansion and calculate its Hausdorff dimension for the case where q≫ (3+5)/2.

UR - https://www.scopus.com/pages/publications/84864463038

U2 - 10.1112/S0025579312000083

DO - 10.1112/S0025579312000083

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JO - Mathematika

JF - Mathematika

IS - 2

ER -

Unique expansion of points of a class of self-similar sets with overlaps

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