The Pisot Conjecture for $\beta$-substitutions
Dynamical Systems
2016-09-28 v2 Number Theory
Abstract
We prove the Pisot Conjecture for beta-substitutions: If beta is a Pisot number, the tiling dynamical system associated with the beta-substitution has pure discrete spectrum. As corollaries: (1) arithmetical coding of the hyperbolic solenoidal automorphism associated with the companion matrix of the minimal polynomial of any Pisot number is almost everywhere one-to-one; and (2) every Pisot number is weakly finitary.
Cite
@article{arxiv.1505.04408,
title = {The Pisot Conjecture for $\beta$-substitutions},
author = {Marcy Barge},
journal= {arXiv preprint arXiv:1505.04408},
year = {2016}
}
Comments
Incorrect comment removed from Section 2, some typos fixed