Substitutive Arnoux-rauzy sequences have pure discrete spectrum

Valérie Berthé (1) , Timo Jolivet (1) , Anne Siegel (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Dyliss - Dynamics, Logics and Inference for biological Systems and Sequences

We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental do- main with fractal boundary (a Rauzy fractal) for this toral translation.

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

Valérie Berthé, Timo Jolivet, Anne Siegel. Substitutive Arnoux-rauzy sequences have pure discrete spectrum. Uniform Distribution Theory, 2012, 7 (1), pp.173-197. ⟨hal-00750209⟩