Lipschitz equivalence of self-similar sets with triangular pattern

被引：0
|
作者：
ZhiYong Zhu
Ying Xiong
LiFeng Xi
机构：
[1] Huazhong University of Science and Technology,School of Mathematics and Statistics
[2] South China University of Technology,Department of Mathematics
[3] Zhejiang Wanli University,Institute of Mathematics
来源：
Science China Mathematics | 2011年 / 54卷
关键词：
fractal; Lipschitz equivalence; triangular pattern; self-similar set; 28A80;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.
引用
收藏
页码：1019 / 1026
页数：7
相关论文
共 50 条
  • [41] 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
  • [42] Average distances on self-similar sets and higher order average distances of self-similar measures
    D. Allen
    H. Edwards
    S. Harper
    L. Olsen
    Mathematische Zeitschrift, 2017, 287 : 287 - 324
  • [43] Self-similar sets and fractals generated by Ciric type operators
    Petrusel, Adrian
    Soos, Anna
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2015, 8 (06): : 1048 - 1058
  • [44] ARITHMETIC REPRESENTATIONS OF REAL NUMBERS IN TERMS OF SELF-SIMILAR SETS
    Jiang, Kan
    Xi, Lifeng
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2019, 44 : 1111 - 1129
  • [45] A CRITERION FOR SELF-SIMILAR SETS TO BE TOTALLY DISCONNECTED
    Luo, Jun
    Xiong, Dong Hong
    ANNALES FENNICI MATHEMATICI, 2021, 46 (02): : 1155 - 1159
  • [46] C*-algebras associated with self-similar sets
    Kajiwara, Tsuyoshi
    Watatani, Yasuo
    JOURNAL OF OPERATOR THEORY, 2006, 56 (02) : 225 - 247
  • [47] Self-similar sets with initial cubic patterns
    Xi, Li-Feng
    Xiong, Ying
    COMPTES RENDUS MATHEMATIQUE, 2010, 348 (1-2) : 15 - 20
  • [48] ON A KIND OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS
    Kong, D.
    Yao, Y.
    ACTA MATHEMATICA HUNGARICA, 2021, 163 (02) : 601 - 622
  • [49] On the Assouad dimension of self-similar sets with overlaps
    Fraser, J. M.
    Henderson, A. M.
    Olson, E. J.
    Robinson, J. C.
    ADVANCES IN MATHEMATICS, 2015, 273 : 188 - 214
  • [50] On a kind of self-similar sets with complete overlaps
    D. Kong
    Y. Yao
    Acta Mathematica Hungarica, 2021, 163 : 601 - 622
12345