ASSOUAD-MINIMALITY OF MORAN SETS UNDER QUASI-LIPSCHITZ MAPPINGS

被引：8

作者：

Xi, Lifeng ^{[1
]}

Deng, Juan ^{[2
]}

Wen, Zhiying ^{[3
]}

机构：

[1] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518000, Peoples R China

[3] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2017年 / 25卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Fractal; Moran Set; Assouad Dimension; Quasi-Lipschitz Mapping; EQUIVALENCE; DIMENSION;

D O I：

10.1142/S0218348X17500372

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The quasi-Lipschitz mappings, weaker than the bi-Lipschitz mappings, preserve Hausdorff, packing and box dimensions, but change Assouad dimension dim(A)(.). In this paper, for Moran fractals, we investigate the change of their Assouad dimension under the quasi-Lipschitz mappings. We study a class of Moran set which is quasi-Lipschitz Assouad-minimal, i.e. for any E in the class, dimA f(E) >= dim(A)(E) for all quasi-Lipschitz mappings f defined on E. For another class of Moran sets, we prove that for any F in the class, inf(g) dim(A) g(F) = dimqA F, where the infimum is taken over all quasi-Lipschitz mappings g defined on F, and dim(q)A(.) is the quasi-Assouad dimension introduced in [F. Lu and L. F. Xi, Quasi-Assouad dimension of fractals, J. Fractal Geom. 3 (2016) 187-215].

引用

页数：8

共 11 条

[1] Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets
WANG Qin XI LiFeng School of Computer Science and Information Technology Zhejiang Wanli University Ningbo ChinaInstitute of Mathematics Zhejiang Wanli University Ningbo China
Science China(Mathematics), 2011, 54 (12) : 2573 - 2582
[2] Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets
Qin Wang
LiFeng Xi
Science China Mathematics, 2011, 54 : 2573 - 2582
[3] Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets
WANG Qin1 & XI LiFeng2
2Institute of Mathematics
Science China Mathematics, 2011, (12) : 2573 - 2582
[4] Quasi-Lipschitz equivalence of quasi Ahlfors-David regular sets
Wang Qin
Xi LiFeng
SCIENCE CHINA-MATHEMATICS, 2011, 54 (12) : 2573 - 2582
[5] Quasi-Lipschitz equivalence of Ahlfors-David regular sets
Wang, Qin
Xi, Lifeng
NONLINEARITY, 2011, 24 (03) : 941 - 950
[6] QUASI-LIPSCHITZ EQUIVALENCE OF SUBSETS OF AHLFORS-DAVID REGULAR SETS
Guo, Qiuli
Li, Hao
Wang, Qin
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2014, 39 (02) : 759 - 769
[7] Non-convex hybrid algorithm for a family of countable quasi-Lipschitz mappings and application
Guan, Jinyu
Tang, Yanxia
Ma, Pengcheng
Xu, Yongchun
Su, Yongfu
FIXED POINT THEORY AND APPLICATIONS, 2015, : 1 - 11
[8] Non-convex hybrid algorithm for a family of countable quasi-Lipschitz mappings and application
Jinyu Guan
Yanxia Tang
Pengcheng Ma
Yongchun Xu
Yongfu Su
Fixed Point Theory and Applications, 2015
[9] Hybrid iterative algorithm for finite families of countable Bregman quasi-Lipschitz mappings with applications in Banach spaces
Chen, Minjiang
Bi, Jianzhi
Su, Yongfu
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015,
[10] Hybrid iterative algorithm for finite families of countable Bregman quasi-Lipschitz mappings with applications in Banach spaces
Minjiang Chen
Jianzhi Bi
Yongfu Su
Journal of Inequalities and Applications, 2015

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