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2014 Dimensions of Fractals Generated by Bi-Lipschitz Maps
Qi-Rong Deng, Sze-Man Ngai
Abstr. Appl. Anal. 2014: 1-12 (2014). DOI: 10.1155/2014/549741


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.


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Qi-Rong Deng. Sze-Man Ngai. "Dimensions of Fractals Generated by Bi-Lipschitz Maps." Abstr. Appl. Anal. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022608
MathSciNet: MR3240548
Digital Object Identifier: 10.1155/2014/549741

Rights: Copyright © 2014 Hindawi


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