Pure discrete spectrum for a class of one-dimensional substitution tiling systems


Marcy Barge


Discrete and Continuous Dynamical Systems - Series A


We prove that if a primitive and non-periodic substitution is injective on initial letters, constant on final letters, and has Pisot inflation, then the ℝ-action on the corresponding tiling space has pure discrete spectrum. As a consequence, all β-substitutions for β a Pisot simple Parry number have tiling dynamical systems with pure discrete spectrum, as do the Pisot systems arising, for example, from substitutions associated with the Jacobi-Perron and Brun continued fraction algorithms.



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