Dimensions of Fractals Generated by Bi-Lipschitz Maps
Document Type
Article
Publication Date
2014
Publication Title
Abstract and Applied Analysis
DOI
10.1155/2014/549741
Abstract
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.
Recommended Citation
Deng, Qi-Rong, Sze-Man Ngai.
2014.
"Dimensions of Fractals Generated by Bi-Lipschitz Maps."
Abstract and Applied Analysis, 2014.
doi: 10.1155/2014/549741
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/306
Comments
Copyright © 2014 Qi-Rong Deng and Sze-Man Ngai. This is an open access article distributed under theCreative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article obtained from Abstract and Applied Analysis.