Weak separation properties for self-similar sets

被引:89
|
作者
Zerner, MPW
机构
关键词
self-similar sets; fractals; weak separation property;
D O I
10.1090/S0002-9939-96-03527-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We develop a theory for self-similar sets in R(s) that fulfil the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson.
引用
收藏
页码:3529 / 3539
页数:11
相关论文
共 50 条
  • [1] SEPARATION PROPERTIES FOR SELF-SIMILAR SETS
    SCHIEF, A
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 122 (01) : 111 - 115
  • [2] From Self-Similar Groups to Self-Similar Sets and Spectra
    Grigorchuk, Rostislav
    Nekrashevych, Volodymyr
    Sunic, Zoran
    FRACTAL GEOMETRY AND STOCHASTICS V, 2015, 70 : 175 - 207
  • [3] WEAK SELF-SIMILAR SETS IN SEPARABLE COMPLETE METRIC SPACES
    Aswathy, R. K.
    Mathew, Sunil
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2017, 25 (02)
  • [4] Self-similar sets in doubling spaces
    Balogh, Zoltan M.
    Rohner, Heiner
    ILLINOIS JOURNAL OF MATHEMATICS, 2007, 51 (04) : 1275 - 1297
  • [5] Multiplication on self-similar sets with overlaps
    Tian, Li
    Gu, Jiangwen
    Ye, Qianqian
    Xi, Lifeng
    Jiang, Kan
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 478 (02) : 357 - 367
  • [6] Curvature Densities of Self-Similar Sets
    Rataj, Jan
    Zaehle, Martina
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2012, 61 (04) : 1425 - 1449
  • [7] Self-similar Sets as Hyperbolic Boundaries
    Lau, Ka-Sing
    Wang, Xiang-Yang
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) : 1777 - 1795
  • [8] Multifractal formalism for self-similar measures with weak separation condition
    Feng, De-Jun
    Lau, Ka-Sing
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2009, 92 (04): : 407 - 428
  • [9] Irrational self-similar sets
    Jia, Qi
    Li, Yuanyuan
    Jiang, Kan
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2022, 100 (3-4): : 461 - 472
  • [10] On singularity of energy measures on self-similar sets
    Hino, M
    PROBABILITY THEORY AND RELATED FIELDS, 2005, 132 (02) : 265 - 290