QUASI-LOWER DIMENSION AND QUASI-LIPSCHITZ MAPPING-Reference-Cited by-同舟云学术

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QUASI-LOWER DIMENSION AND QUASI-LIPSCHITZ MAPPING

Published:2017-05-18 Issue:03 Volume:25 Page:1750034
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

CHEN HAIPENG¹,DU YALI²,WEI CHUN³

Affiliation:

1. Department of Mathematics, South China University of Technology, Guangzhou 510641, P. R. China

2. Institute of Mathematics and Statistics, University of Sao Paulo, Sao Paulo 05508-090 SP, Brazil

3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, P. R. China

Abstract

In this paper, we show that the lower dimension is not invariant under quasi-Lipschitz mapping, and then we find an invariant named the quasi-lower dimension. We also compute the quasi-lower dimension of a class of sets defined by digit restrictions, and then give an example to distinguish the quasi-lower dimension and other dimensions.

Funder

NSFC

Fundamental Research Funds for the Central Universities

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X17500347

Reference19 articles.

1. Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios

2. Classification of a quasi-circles by Hausdorff dimension

3. On the Lipschitz equivalence of Cantor sets

4. Relations among whitney sets, self-similar arcs and quasi-arcs

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1. Box-counting dimensions of popcorn subsets;Journal of Mathematical Analysis and Applications;2023-08

2. FRACTAL DIMENSIONS OF SETS DEFINED BY DIGIT RESTRICTIONS IN ℝ2;Fractals;2023-01

3. THE THICKNESS AND QUASISYMMETRICAL EQUIVALENCE OF THE SETS DEFINED BY DIGIT RESTRICTIONS;Fractals;2023-01

4. Assouad-like dimensions of a class of random Moran measures;Journal of Mathematical Analysis and Applications;2022-04

5. Intermediate Assouad-like dimensions;Journal of Fractal Geometry;2021-04-30

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