Dimensions of fractals generated by bi-Lipschitz maps
type: Item
instance of: scholarly article
title: Dimensions of fractals generated by bi-Lipschitz maps
zbMATH Open document ID: 1474.28007
DOI: 10.1155/2014/549741
author: Qi-Rong Deng
author: Sze-Man Ngai
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: On the class of iterated function systems of bi-Lipschitz mappings that are contractions with respect to some metrics, we introduce a logarithmic distortion property, which is weaker than the well-known bounded distortion property. By assuming this property, we prove the equality of the Hausdorff and box dimensions of the attractor. We also obtain a formula for the dimension of the attractor in terms of certain modified topological pressure functions, without imposing any separation condition. As an application, we prove the equality of Hausdorff and box dimensions for certain iterated function systems consisting of affine maps and nonsmooth maps.
Mathematics Subject Classification ID: 28A78
Mathematics Subject Classification ID: 37F35
zbMATH DE Number: 7022608
Wikidata QID: Q59039418
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/549741
OpenAlex ID: W2070706494
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description: scientific article; zbMATH DE number 7022608