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Substitutive Arnoux-Rauzy sequences have pure discrete spectrum (1108.5574v2)
Published 29 Aug 2011 in math.DS, cs.DM, and math.CO
Abstract: 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.