arXiv Analytics

Sign in

arXiv:1108.5574 [math.DS]AbstractReferencesReviewsResources

Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

Valérie Berthé, Timo Jolivet, Anne Siegel

Published 2011-08-29, updated 2014-06-26Version 2

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.

Comments: 19 pages, v2 includes some corrections to match the published version, and a mistake in the graph of Fig. 1 has been corrected
Journal: Uniform Distribution Theory 7 (2012), no. 1, 173-197
Categories: math.DS, cs.DM, math.CO
Related articles: Most relevant | Search more
arXiv:2102.02497 [math.DS] (Published 2021-02-04)
A Rauzy fractal unbounded in all directions of the plane
arXiv:2401.06732 [math.DS] (Published 2024-01-12)
Rauzy fractals of random substitutions
arXiv:1711.03535 [math.DS] (Published 2017-11-08)
Tree substitutions and Rauzy fractals

Links

Toolbox