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

Bédaride, Nicolas; Bertazzon, Jean-François

doi:10.1090/tran/6948

An example of PET. Computation of the Hausdorff dimension of the aperiodic set
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by Nicolas Bédaride and Jean-François Bertazzon PDF

Trans. Amer. Math. Soc. 370 (2018), 357-391 Request permission

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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