An Application of Topological Multiple Recurrence to Tiling
Dynamical Systems
2008-09-09 v1
Abstract
We show that given any tiling of Euclidean space, any geometric patterns of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated version of the pattern. The rather simple proof uses Furstenberg's topological multiple recurrence theorem.
Cite
@article{arxiv.0809.1421,
title = {An Application of Topological Multiple Recurrence to Tiling},
author = {Rafael de la Llave and Alistair Windsor},
journal= {arXiv preprint arXiv:0809.1421},
year = {2008}
}