Local Theory of Regular Systems and Delone Sets

We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classica...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2024-06, Vol.325 (1), p.120-135
Main Author: Dolbilin, N. P.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We survey the results of the local theory of regular systems that are related to estimating the regularity radius. We also discuss recent results on local groups in arbitrary Delone sets in the plane and in the three-dimensional space, including new theorems and conjectures generalizing the classical statement on the absence of fivefold rotations in lattices.
ISSN:0081-5438
1531-8605
DOI:10.1134/S008154382402007X