Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2011
- DOI:
- 10.48550/arXiv.1108.5574
- arXiv:
- arXiv:1108.5574
- Bibcode:
- 2011arXiv1108.5574B
- Keywords:
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- Mathematics - Dynamical Systems;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics
- E-Print:
- 19 pages, v2 includes some corrections to match the published version, and a mistake in the graph of Fig. 1 has been corrected