On the structures and dimensions of Moran sets
type: Item
instance of: scholarly article
title: On the structures and dimensions of Moran sets
zbMATH Open document ID: 0976.28002
DOI: 10.1007/BF02884183
author: Hui Rao
author: Zhiying Wen
author: Jun Wu
author: Hua Su
published in: Science in China. Series A
publication date: 2001-08-30T00:00:00Z
review text: In this paper the authors investigate the Moran sets which are defined by geometric fashion that distinguishes the classical self-similar sets from the following points: (i) the placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; (iii) the lower limit of the contraction ratios permits zero. They determine the Hausdorff, packing and upper box-counting dimensions of the Moran sets by net and net measure techniques.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 28A78
zbMATH DE Number: 1542540
zbMATH Keywords: Moran set
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: packing dimension
zbMATH Keywords: box-counting dimension
MaRDI profile type: Publication
cites work: Q3731958
cites work: Q3995301
cites work: Q3974721
cites work: The Hausdorff dimension of general Sierpiński carpets
cites work: Dimensions and Measures in Infinite Iterated Function Systems
cites work: A class of self-similar fractals with overlap structure
cites work: On the dimension of deterministic and random Cantor-like sets, symbolic dynamics, and the Eckmann-Ruelle conjecture
cites work: Some dimensional results for homogeneous Moran sets
cites work: Q5844839
cites work: The net measure properties of symmetric Cantor sets and their applications
full work available at URL: https://doi.org/10.1007/bf02884183
OpenAlex ID: W2002186050
description: scientific article; zbMATH DE number 1542540