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arXiv · 1108.5574

Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

Valérie Berthé·Timo Jolivet·Anne Siegel
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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.

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Valérie Berthé, Timo Jolivet, Anne Siegel. 2014-06-26. Substitutive Arnoux-Rauzy sequences have pure discrete spectrum. https://arxiv.org/abs/1108.5574

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