Abstract
It is proved that every pseudo-self-affine tiling in ℝd is mutually locally derivable with a self-affine tiling. A characterization of pseudo-self-similar tilings in terms of derived Voronoï 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. Bibliography: 18 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 198–213.
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Solomyak, B. Pseudo-self-affine tilings in ℝd . J Math Sci 140, 452–460 (2007). https://doi.org/10.1007/s10958-007-0452-3
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DOI: https://doi.org/10.1007/s10958-007-0452-3