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Representation of nonunimodular substitution dynamical systems. (Représentation des systèmes dynamiques substitutifs non unimodulaires.) (French) Zbl 1052.37009
The author shows that the “strong coincidence property” suffices for a Pisot substitutive dynamical system to be isomorphic (in measure) to an exchange of pieces in some self-similar compact set of a certain type. In particular any Pisot substitutive system is a finite extension of its maximal equicontinuous factor. Please note that the reference [Sie 02] has appeared [A. Siegel, Ann. Inst. Fourier 54, 289–299 (2004)].

MSC:
37B10 Symbolic dynamics
11B85 Automata sequences
68R15 Combinatorics on words
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
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