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arXiv · 1512.01632

An example of PET. Computation of the Hausdorff dimension of the aperiodic set

Nicolas Bédaride·Jean-François Bertazzon
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Abstract

We introduce a family of piecewise isometries. This family is similar to the ones studied by Hooper and Schwartz. We prove that a renormalization scheme exists inside this family and compute the Hausdorff dimension of the discontinuity set. The methods use some cocycles and a continued fraction algorithm.

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Nicolas Bédaride, Jean-François Bertazzon. 2015-12-05. An example of PET. Computation of the Hausdorff dimension of the aperiodic set. https://arxiv.org/abs/1512.01632

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