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

作者:Zou, Yuru; Lu, Jian; Li, Wenxia*
来源:Mathematika, 2012, 58(2): 371-388.
DOI:10.1112/S0025579312000083

摘要

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 root 5)/2.