Resumen de Hausdorff Dimension of the Exceptional Set of Interval Piecewise Affine Contractions

José Pedro Gaivao

• Let I = [0, 1), −1 <λ< 1 and f : I → I be a piecewise λ-affine map of the interval I. The exceptional set E f of f is the set of parameters δ ∈ R such that Rδ ◦ f is not asymptotically periodic, where Rδ : I → I is the rotation of angle δ. In this paper we prove that E f has zero Hausdorff dimension. We derive this result from a more general theorem concerning piecewise Lipschitz contractions on R that has independent interest.