Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
  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 domain with fractal boundary (a Rauzy fractal) for this toral translation. 
Val\'erie Berth\'e, Timo Jolivet, Anne Siegel
math.DS cs.DM math.CO