Conditional bi-Lipschitz equivalence of self-similar sets

2021 ◽  
Vol 153 ◽  
pp. 111479
Author(s):  
Qi Jia ◽  
Chen Chen ◽  
Ying Ma ◽  
Lei Lei ◽  
Kan Jiang
Keyword(s):  
Lipschitz Equivalence ◽  
Self Similar

scholarly journals Lipschitz equivalence of self-similar sets and hyperbolic boundaries II

2015 ◽  
Vol 2 (1) ◽  
pp. 53-79 ◽  
Author(s):  
Guo-Tai Deng ◽  
Ka-Sing Lau ◽  
Jun Luo
Keyword(s):  
Lipschitz Equivalence ◽  
Self Similar

scholarly journals Lipschitz equivalence of a class of self-similar sets with complete overlaps

2012 ◽  
Vol 37 ◽  
pp. 229-243 ◽  
Author(s):  
Qiuli Guo ◽  
Hao Li ◽  
Qin Wang ◽  
Lifeng Xi
Keyword(s):  
Lipschitz Equivalence ◽  
Self Similar

SELF-SIMILARITY AND LIPSCHITZ EQUIVALENCE OF UNIONS OF CANTOR SETS

Fractals ◽  
2018 ◽  
Vol 26 (05) ◽  
pp. 1850061
Author(s):  
CHUNTAI LIU
Keyword(s):  
Cantor Set ◽  
Cantor Sets ◽  
Necessary And Sufficient Condition ◽  
Self Similarity ◽  
Lipschitz Equivalence ◽  
Fractal Sets ◽  
Strong Separation ◽  
Self Similar ◽  
Strong Separation Condition ◽  
Necessary And Sufficient

Self-similarity and Lipschitz equivalence are two basic and important properties of fractal sets. In this paper, we consider those properties of the union of Cantor set and its translate. We give a necessary and sufficient condition that the union is a self-similar set. Moreover, we show that the union satisfies the strong separation condition if it is of the self-similarity. By using the augment tree, we characterize the Lipschitz equivalence between Cantor set and the union of Cantor set and its translate.

Lipschitz equivalence of self-similar sets with triangular pattern

2011 ◽  
Vol 54 (5) ◽  
pp. 1019-1026 ◽  
Author(s):  
ZhiYong Zhu ◽  
Ying Xiong ◽  
LiFeng Xi
Keyword(s):  
Lipschitz Equivalence ◽  
Self Similar

LIPSCHITZ EQUIVALENCE OF TOTALLY DISCONNECTED GENERAL SIERPINSKI TRIANGLES

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550013 ◽  
Author(s):  
ZHI-YONG ZHU
Keyword(s):  
Hausdorff Dimension ◽  
Compact Set ◽  
Lipschitz Equivalence ◽  
Self Similar ◽  
Totally Disconnected

Given an integer n ≥ 2 and an ordered pair (A, B) with A ⊂ {k1α + k2β : k1 + k2 ≤ n - 1 and k1, k2 ∈ ℕ ∪{0}} and B ⊂ {k1α + k2β : 2 ≤ k1 + k2 ≤ n and k1, k2 ∈ ℕ}, where [Formula: see text]. Let T ≔ T(A, B) be unique compact set of ℝ2 satisfying the set equation: T = [(T+A)∪(B-T)]/n. In this paper, we show that such self-similar sets which are totally disconnected are determined to within Lipschitz equivalence by their Hausdorff dimension.

Sign in / Sign up

Export Citation Format

Share Document