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arXiv · 0906.3740

Hausdorff dimension of certain random self--affine fractals

Nuno Luzia
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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.

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Nuno Luzia. 2009-06-19. Hausdorff dimension of certain random self--affine fractals. https://arxiv.org/abs/0906.3740

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