Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

Details Substitutive Arnoux-Rauzy sequences have pure discrete spectrum Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

2011-08-29

arxiv.org/abs/1108.5574v1

Mathematics

Dynamical Systems

21 pages

Scientific paper

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. Such a fractal is obtained as the Hausdorff limit of a sequence of compact planar sets, where each set is the projection of a finite union of faces of unit cubes generated by a multidimensional version of the underlying Arnoux-Rauzy substitution.

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