Hausdorff dimension of certain random self--affine fractals

Details Hausdorff dimension of certain random self--affine fractals Hausdorff dimension of certain random self--affine fractals

2009-06-19

arxiv.org/abs/0906.3740v1

Mathematics

Dynamical Systems

Scientific paper

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.

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