Finite type in measure sense for self-similar sets with overlaps

被引：0
|
作者：
Deng, Juan [1 ]
Wen, Zhiying [2 ]
Xi, Lifeng [3 ,4 ]
机构：
[1] ShenZhen Univ, Dept Math, Shenzhen 518000, Peoples R China
[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China
[3] Ningbo Univ, Dept Math, Ningbo 315211, Peoples R China
[4] Hunan Normal Univ, Minist Educ, Sch Math & Stat, Key Lab Comp & Stochast Math, Changsha 410081, Hunan, Peoples R China
来源：
MATHEMATISCHE ZEITSCHRIFT | 2021年 / 298卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
Self-similar set; Finite type in measure sense; Weak separation condition; Generalized finite type; ITERATED FUNCTION SYSTEMS; SIMILAR FRACTALS; DIMENSION;
D O I：
10.1007/s00209-020-02632-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For self-similar sets with overlaps, we introduce a notion named the finite type in measure sense and reveal its intrinsic relationships with the weak separation condition and the generalized finite type.
引用
收藏
页码：821 / 837
页数：17
相关论文
共 50 条
  • [41] Arithmetic progressions in self-similar sets
    Xi, Lifeng
    Jiang, Kan
    Pei, Qiyang
    FRONTIERS OF MATHEMATICS IN CHINA, 2019, 14 (05) : 957 - 966
  • [42] Self-similar Sets as Hyperbolic Boundaries
    Lau, Ka-Sing
    Wang, Xiang-Yang
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2009, 58 (04) : 1777 - 1795
  • [43] DIMENSIONS OF SUMS WITH SELF-SIMILAR SETS
    Oberlin, Daniel
    Oberlin, Richard
    COLLOQUIUM MATHEMATICUM, 2017, 147 (01) : 43 - 54
  • [44] AN ANSWER TO A CONJECTURE ON SELF-SIMILAR SETS
    Baoguo Jia (Zhongshan University
    AnalysisinTheoryandApplications, 2007, (01) : 9 - 15
  • [45] Trigonometric series and self-similar sets
    Li, Jialun
    Sahlsten, Tuomas
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2022, 24 (01) : 341 - 368
  • [46] Lipschitz equivalence of self-similar sets and hyperbolic boundaries
    Luo, Jun Jason
    Lau, Ka-Sing
    ADVANCES IN MATHEMATICS, 2013, 235 : 555 - 579
  • [47] The interior of randomly perturbed self-similar sets on the line
    Dekking, Michel
    Simon, Karoly
    Szekely, Balazs
    Szekeres, Nora
    ADVANCES IN MATHEMATICS, 2024, 448
  • [48] RESONANCE BETWEEN SELF-SIMILAR SETS AND THEIR UNIVOQUE SETS
    Chen, Chen
    Ma, Ying
    Lei, Lei
    Gareeb, Mohammad
    Jiang, Kan
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2021, 29 (05)
  • [49] Average distances on self-similar sets and higher order average distances of self-similar measures
    Allen, D.
    Edwards, H.
    Harper, S.
    Olsen, L.
    MATHEMATISCHE ZEITSCHRIFT, 2017, 287 (1-2) : 287 - 324
  • [50] Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets
    Winter, Steffen
    ADVANCES IN MATHEMATICS, 2015, 274 : 285 - 322
12345