Singularity and L2-dimension of self-similar measures

被引：1
|
作者：
Ngai, Sze-Man [1 ,2 ]
机构：
[1] Georgia So Univ, Dept Math Sci, Statesboro, GA 30460 USA
[2] Hunan Normal Univ, Coll Math & Comp Sci, Changsha 410081, Hunan, Peoples R China
来源：
CHAOS SOLITONS & FRACTALS | 2012年 / 45卷 / 03期
关键词：
WEAK SEPARATION CONDITION; ITERATED FUNCTION SYSTEMS; BERNOULLI CONVOLUTIONS; DIMENSION; FRACTALS; OVERLAPS; FAMILY;
D O I：
10.1016/j.chaos.2011.12.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study self-similar measures defined by non-uniformly contractive iterated function systems of similitudes with overlaps. In the case the contraction ratios of the similitudes are exponentially commensurable, we describe a method to compute the L-2-dimension of the associated self-similar measures. Our result allows us to determine the singularity of some of such measures. (C) 2011 Elsevier Ltd. All rights reserved.
引用
收藏
页码：256 / 265
页数：10
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