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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Article dans une revue
Uniform Distribution Theory, Mathematical Institute of the Slovak Academy of Sciences, 2012, 7 (1), pp.173-197. 〈http://www.boku.ac.at/MATH/udt/vol07/no1/09BertJolSieg29-11.pdf〉
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https://hal.inria.fr/hal-00750209
Contributeur : Anne Siegel <>
Soumis le : vendredi 9 novembre 2012 - 11:27:22
Dernière modification le : mercredi 16 mai 2018 - 11:23:35

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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. 〈http://www.boku.ac.at/MATH/udt/vol07/no1/09BertJolSieg29-11.pdf〉. 〈hal-00750209〉

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