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Journal Articles Uniform Distribution Theory Year : 2012

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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Dates and versions

hal-00750209 , version 1 (09-11-2012)

Identifiers

  • HAL Id : hal-00750209 , version 1

Cite

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