Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

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.

19 pages, v2 includes some corrections to match the published version, and a mistake in the graph of Fig. 1 has been corrected

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