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

Nicolas Bedaride (1) , Jean François Bertazzon (2)

1 I2M - Institut de Mathématiques de Marseille
2 Lycée Notre-Dame de Sion

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.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]; Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Nicolas Bedaride, Jean François Bertazzon. An example of PET. Computation of the Hausdorff dimension of the aperiodic set. Transactions of the American Mathematical Society, 2018, 370, pp.357-391. ⟨10.1090/tran/6948⟩. ⟨hal-01255426⟩