ON THE DIMENSION OF SELF-SIMILAR SETS-Reference-Cited by-同舟云学术

ON THE DIMENSION OF SELF-SIMILAR SETS

Published:2002-03 Issue:01 Volume:10 Page:59-65
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

SIMON KÁROLY¹,SOLOMYAK BORIS²

Affiliation:

1. Department of Stochastics, Institute of Mathematics, Technical University of Budapest, 1521 Budapest P.O. Box 91, Hungary

2. Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA

Abstract

We extend a theorem of Falconer to give a complete result on the dimension and Lebesgue measure of typical self-similar attractors on the line. Further, we present some examples to point out that in higher dimensions, one cannot expect the same result in this generality.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X02000963

Reference11 articles.

1. Products of random matrices and computer image generation

2. The Hausdorff dimension of self-affine fractals

3. Measure and dimension for some fractal families

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