ON THE DIMENSION OF SELF-SIMILAR SETS
Authors:
- 1 March 2002
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Fractals
- Vol. 10 (01) , 59-65
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.Keywords
This publication has 8 references indexed in Scilit:
- Measure and dimension for some fractal familiesMathematical Proceedings of the Cambridge Philosophical Society, 1998
- Dimensions and measures of quasi self-similar setsProceedings of the American Mathematical Society, 1989
- On the Hausdorff dimension of some fractal setsStudia Mathematica, 1989
- The Hausdorff dimension of self-affine fractalsMathematical Proceedings of the Cambridge Philosophical Society, 1988
- The Hausdorff dimension of some fractals and attractors of overlapping constructionJournal of Statistical Physics, 1987
- Products of random matrices and computer image generation1986
- Representations for real numbers and their ergodic propertiesActa Mathematica Hungarica, 1957
- Some Fundamental Geometrical Properties of Plane Sets of Fractional DimensionsProceedings of the London Mathematical Society, 1954