Self-affine sets with positive Lebesgue measure

被引：11
|
作者：
Dajani, Karma [1 ]
Jiang, Kan [1 ]
Kempton, Tom [1 ]
机构：
[1] Univ Utrecht, Dept Math, Utrecht, Netherlands
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2014年 / 25卷 / 04期
关键词：
Overlapping self-affine sets; Iterated function systems; beta-expansions; BETA-EXPANSIONS;
D O I：
10.1016/j.indag.2014.04.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a 'simultaneous beta-expansion' of different numbers in different bases. (C) 2014 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：774 / 784
页数：11
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