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.
- Pub Date:
- August 2011
- Mathematics - Dynamical Systems;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics
- 19 pages, v2 includes some corrections to match the published version, and a mistake in the graph of Fig. 1 has been corrected