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arXiv · 1505.04408

The Pisot Conjecture for $\beta$-substitutions

Marcy Barge
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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.

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Marcy Barge. 2015-05-17. The Pisot Conjecture for $\beta$-substitutions. https://doi.org/10.1017/etds.2016.44

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