Pseudo-self-affine tilings in R^d

Details Pseudo-self-affine tilings in R^d Pseudo-self-affine tilings in R^d

2005-10-02

arxiv.org/abs/math/0510014v1

Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 326 (2005), Teor. Predst. Din. Sist. Komb. i Algoritm. Metod

Mathematics

Dynamical Systems

16 pages, submitted to a volume dedicated to A. M. Vershik

Scientific paper

It is proved that every pseudo-self-affine tiling in R^d is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoi tessellations is a corollary. Previously, these results were obtained in the planar case, jointly with Priebe Frank. The new approach is based on the theory of graph-directed iterated function systems and substitution Delone sets developed by Lagarias and Wang.

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