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Tilings from some non-irreducible, Pisot substitutions. (English) Zbl 1153.37323

Summary: A generating method of self-affine tilings for Pisot, unimodular, irreducible substitutions, as well as the fact that the associated substitution dynamical systems are isomorphic to rotations on the torus are established in P. Arnoux and S. Ito [Bull. Belg. Math. Soc. - Simon Stevin 8, No. 2, 181–207 (2001; Zbl 1007.37001)]. The aim of this paper is to extend these facts in the case where the characteristic polynomial of a substitution is non-irreducible for a special class of substitutions on five letters. Finally we show that the substitution dynamical systems for this class are isomorphic to induced transformations of rotations on the torus.

MSC:

37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)

Citations:

Zbl 1007.37001
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