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Pure discrete spectrum dynamical system and periodic tiling associated with a substitution. (English) Zbl 1083.37009
This survey studies symbolic dynamical systems associated with a substitution of Pisot type. The goal is to find a computable sufficient condition in order to have a pure discrete spectrum. The author uses a formal and algebraic point of view instead of the usual measurable techniques to investigate the questions of self-similarity and pure discrete spectrum.

MSC:
37B10 Symbolic dynamics
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
47A35 Ergodic theory of linear operators
28A80 Fractals
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