Pseudo-self-affine tilings in R^d
Dynamical Systems
2011-07-20 v1 Metric Geometry
Abstract
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.
Cite
@article{arxiv.math/0510014,
title = {Pseudo-self-affine tilings in R^d},
author = {Boris Solomyak},
journal= {arXiv preprint arXiv:math/0510014},
year = {2011}
}
Comments
16 pages, submitted to a volume dedicated to A. M. Vershik