Hausdorff dimension of certain random self--affine fractals
Dynamical Systems
2009-06-23 v1
Abstract
In this work we are interested in the self--affine fractals studied by Gatzouras and Lalley and by the author which generalize the famous general Sierpinski carpets studied by Bedford and McMullen. We give a formula for the Hausdorff dimension of sets which are randomly generated using a finite number of self-affine transformations each one generating a fractal set as mentioned before, with some technical hypotheses. The choice of the transformation is random according to a Bernoulli measure. The formula is given in terms of the variational principle for the dimension.
Keywords
Cite
@article{arxiv.0906.3740,
title = {Hausdorff dimension of certain random self--affine fractals},
author = {Nuno Luzia},
journal= {arXiv preprint arXiv:0906.3740},
year = {2009}
}