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

Marcy Barge

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arXiv · 1403.7826

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

Marcy Barge

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Abstract

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 beta-substitutions for beta a Pisot simple Parry number have tiling dynamical systems with pure discrete spectrum, as do the Pisot systems arising, for example, from the Jacobi-Perron and Brun continued fraction expansions.

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Marcy Barge. 2014-03-30. Pure discrete spectrum for a class of one-dimensional substitution tiling systems. https://arxiv.org/abs/1403.7826

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