Deformation of Delone dynamical systems and pure point diffraction
Dynamical Systems
2007-10-04 v2 Mathematical Physics
math.MP
Abstract
This paper deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and aperiodic order, and important subclasses of them exhibit pure point diffraction spectra. We discuss the relevant framework and recall fundamental results and examples. In particular, we show that pure point diffraction is stable under ``equivariant'' local perturbations and discuss various examples,including deformed model sets. A key step in the proof of stability consists in transforming the problem into a question on factors of dynamical systems.
Cite
@article{arxiv.math/0404155,
title = {Deformation of Delone dynamical systems and pure point diffraction},
author = {Michael Baake and Daniel Lenz},
journal= {arXiv preprint arXiv:math/0404155},
year = {2007}
}
Comments
25 pages; revised version with minor corrections, an extended summary of the topic, and further references