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