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 do- main with fractal boundary (a Rauzy fractal) for this toral translation.
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https://hal.inria.fr/hal-00750209
Contributor : Anne Siegel <>
Submitted on : Friday, November 9, 2012 - 11:27:22 AM
Last modification on : Friday, January 4, 2019 - 5:32:57 PM

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  • HAL Id : hal-00750209, version 1

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

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