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UNIQUE EXPANSION OF POINTS OF A CLASS OF SELF-SIMILAR SETS WITH OVERLAPS

Part of: Approximations and expansions

Published online by Cambridge University Press:  25 April 2012

Yuru Zou ,
Jian Lu  and
Wenxia Li
Yuru Zou
Affiliation:
College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, PR China (email: [email protected])
Jian Lu
Affiliation:
College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, PR China (email: [email protected])
Wenxia Li*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, PR China (email: [email protected])
*
*Wenxia Li is the corresponding author.
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Abstract

For q>1, the set Fq 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 Fq whose elements have a unique expansion and calculate its Hausdorff dimension for the case where .

MSC classification

Secondary: 41A99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 58 , Issue 2 , July 2012 , pp. 371 - 388
Copyright
Copyright © University College London 2012

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