Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

Anne Siegel; Timo Jolivet; Val\'erie Berth\'e

arxiv: 1108.5574 · v2 · pith:OS4FZGUHnew · submitted 2011-08-29 · 🧮 math.DS · cs.DM· math.CO

Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

Val\'erie Berth\'e , Timo Jolivet , Anne Siegel This is my paper

classification 🧮 math.DS cs.DMmath.CO

keywords arnoux-rauzyfractalsubstitutivetoraltranslationboundaryconjugateconstruction

0 comments

read the original 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 domain with fractal boundary (a Rauzy fractal) for this toral translation.

This paper has not been read by Pith yet.

Substitutive Arnoux-Rauzy sequences have pure discrete spectrum

discussion (0)