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

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.

39 pages. To appear Transactions of the AMS. 2016