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
  • [1] Lipschitz equivalence of self-similar sets with triangular pattern
    ZHU ZhiYong1
    2Department of Mathematics
    3Institute of Mathematics
    Science China(Mathematics), 2011, 54 (05) : 1019 - 1026
  • [2] Lipschitz equivalence of self-similar sets with triangular pattern
    Zhu ZhiYong
    Xiong Ying
    Xi LiFeng
    SCIENCE CHINA-MATHEMATICS, 2011, 54 (05) : 1019 - 1026
  • [3] Lipschitz equivalence of dust-like self-similar sets
    Xi, Li-Feng
    MATHEMATISCHE ZEITSCHRIFT, 2010, 266 (03) : 683 - 691
  • [4] Lipschitz equivalence of dust-like self-similar sets
    Li-Feng Xi
    Mathematische Zeitschrift, 2010, 266 : 683 - 691
  • [5] Lipschitz equivalence of self-similar sets and hyperbolic boundaries
    Luo, Jun Jason
    Lau, Ka-Sing
    ADVANCES IN MATHEMATICS, 2013, 235 : 555 - 579
  • [6] LIPSCHITZ EQUIVALENCE OF SELF-SIMILAR SETS WITH EXACT OVERLAPS
    Jiang, Kan
    Wang, Songjing
    Xi, Lifeng
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2018, 43 : 905 - 912
  • [7] LIPSCHITZ EQUIVALENCE OF A CLASS OF SELF-SIMILAR SETS
    Chen, Xiu
    Jiang, Kan
    Li, Wenxia
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2017, 42 (02) : 585 - 591
  • [8] LIPSCHITZ EQUIVALENCE OF A CLASS OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS
    Guo, Qiuli
    Li, Hao
    Wang, Qin
    Xi, Lifeng
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2012, 37 (01) : 229 - 243
  • [9] Lipschitz equivalence of self-similar sets and hyperbolic boundaries II
    Deng, Guo-Tai
    Lau, Ka-Sing
    Luo, Jun Jason
    JOURNAL OF FRACTAL GEOMETRY, 2015, 2 (01) : 53 - 79
  • [10] Lipschitz equivalence of self-similar sets with touching structures
    Ruan, Huo-Jun
    Wang, Yang
    Xi, Li-Feng
    NONLINEARITY, 2014, 27 (06) : 1299 - 1321
12345