Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices

For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient condition of Rauzy, of an infinite family of non-trivial bounded rem...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-05, Vol.212 (1), p.189-201
Main Authors: Haynes, Alan, Koivusalo, Henna
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:For any irrational cut-and-project setup, we demonstrate a natural infinite family of windows which gives rise to separated nets that are each bounded distance to a lattice. Our proof provides a new construction, using a sufficient condition of Rauzy, of an infinite family of non-trivial bounded remainder sets for any totally irrational toral rotation in any dimension.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1283-z