Separation properties for infinite iterated function systems

被引：0
作者：
Hui Liu
Xiangling Zhu
机构：
[1] JiaYing University,Department of Mathematics
来源：
Journal of Inequalities and Applications | / 2014卷
关键词：
infinite iterated function systems; open set condition; weak separation condition; generalized finite type condition;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the infinite iterated function systems (IFSs) of contractive similitudes with overlaps. We extend the notions of the weak separation condition and the generalized finite type condition for finite IFSs to the infinite case. We show that for an infinite IFS of contractive similitudes the generalized finite type condition implies the weak separation condition.
引用
收藏
相关论文
共 26 条
[1]  
Hutchinson J(1981)Fractals and self-similarity Indiana Univ. Math. J 30 713-747
[2]  
Bandt C(1992)Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure Proc. Am. Math. Soc 114 995-1001
[3]  
Graf S(1994)Separation properties for self-similar sets Proc. Am. Math. Soc 122 111-115
[4]  
Schief A(1999)Iterated function system and Ruelle operator J. Math. Anal. Appl 231 319-344
[5]  
Fan A(2001)Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets Proc. Am. Math. Soc 129 2689-2699
[6]  
Lau K(2002)Separation properties for self-conformal sets Stud. Math 152 33-44
[7]  
Peres Y(1999)Multifractal measures and a weak separation condition Adv. Math 141 45-96
[8]  
Rams M(2007)A generalized finite type condition for iterated function systems Adv. Math 208 647-671
[9]  
Simon K(1996)Weak separation properties for self-similar sets Proc. Am. Math. Soc 124 3529-3539
[10]  
Solomyak B(2002)Iterated function systems of finite type and the weak separation property Proc. Am. Math. Soc 130 483-487
123