The Pisot conjecture for beta-substitutions
Ergodic Theory & Dynamical Systems
We prove the Pisot conjecture for beta-substitutions: if beta is a Pisot number, then the tiling dynamical system. (Omega(Psi beta), R) 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) all Pisot numbers are weakly finitary.
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