Model sets, almost periodic patterns, uniform density and linear maps
Dynamical Systems
2015-12-03 v1 Discrete Mathematics
Metric Geometry
Abstract
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are stable under discretizations of linear maps.
Cite
@article{arxiv.1512.00650,
title = {Model sets, almost periodic patterns, uniform density and linear maps},
author = {Pierre-Antoine Guihéneuf},
journal= {arXiv preprint arXiv:1512.00650},
year = {2015}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:1510.00722