Mathematika

Table of Contents - July 2012 - Volume 58, Issue 02  

Research Article

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

Yuru Zoua1, Jian Lua2 and Wenxia Lia3 c1

a1 College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, PR China (email: yrzou@163.com)

a2 College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, PR China (email: jlu@163.com)

a3 Department of Mathematics, East China Normal University, Shanghai 200241, PR China (email: wxli@math.ecnu.edu.cn)

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 $q\geq (3+\sqrt {5})/{2}$.

(Received January 09 2011)

(Online publication April 25 2012)

MSC (2010)

  • 41A99 (primary)

Correspondence:

c1 Wenxia Li is the corresponding author.