Article
Substitutive Arnoux-Rauzy Sequences Have Pure Discrete Spectrum
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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 do- main with fractal boundary (a Rauzy fractal) for this toral translation.
Keywords
Arnoux-Rauzy substitutions, discrete spectrum, Rauzy fractal.
Citation
Berthe, V., Jolivet, T., & Siegel, A. (2012). Substitutive arnoux-rauzy sequences have pure discrete spectrum. Uniform Distribution Theory, 7(1), 173–197.
V. Berthe, T. Jolivet and A. Siegel, “Substitutive arnoux-rauzy sequences have pure discrete spectrum,” Uniform Distribution Theory, vol. 7, no. 1, pp. 173–197, 2012.
Berthe V, Jolivet T, Siegel A. Substitutive arnoux-rauzy sequences have pure discrete spectrum. Uniform Distribution Theory. 2012;7(1):173–197.
Berthe, V., Jolivet, T. and Siegel, A. (2012), ‘Substitutive arnoux-rauzy sequences have pure discrete spectrum’, Uniform Distribution Theory, 7(1), pp. 173–197.
Berthe, Valerie, et al. “Substitutive Arnoux-rauzy Sequences Have Pure Discrete Spectrum.” Uniform Distribution Theory, vol. 7, no. 1, 2012, pp. 173–197.
Berthe, Valerie, Timo Jolivet, and Anne Siegel. “Substitutive Arnoux-rauzy Sequences Have Pure Discrete Spectrum.” Uniform Distribution Theory 7, no. 1 (2012): 173–197.
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Published by: Engineering Journals
