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

Alan Haynes; Henna L L Koivusalo

doi:10.1007/s11856-016-1283-z

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

Alan Haynes
, Henna L L Koivusalo^*

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

12 Citations (Scopus)

67 Downloads (Pure)

Abstract

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.

Original language	English
Pages (from-to)	189-201
Journal	Israel Journal of Mathematics
Volume	212
DOIs	https://doi.org/10.1007/s11856-016-1283-z
Publication status	Published - 7 Jan 2016

Keywords

Fundamental Domain
Subspace Versus
Irrational Rotation
Rational Subspace

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10.1007/s11856-016-1283-z

Full-text PDF (author’s accepted manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer Verlag at https://doi.org/10.1007/s11856-016-1283-z . Please refer to any applicable terms of use of the publisher.
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Diophantine approximation, chromatic number, and equivalence classes of separated nets
Haynes, A. K. (Principal Investigator)
1/07/13 → 1/07/15
Project: Research
Career Acceleration Fellowship
Haynes, A. K. (Principal Investigator)
1/10/11 → 1/10/13
Project: Research

Dr Henna L L Koivusalo
- henna.koivusalobristol.acuk
- School of Mathematics - Senior Lecturer
Person: Academic

Cite this

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title = "Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices",

abstract = "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.",

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doi = "10.1007/s11856-016-1283-z",

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AU - Haynes, Alan

AU - Koivusalo, Henna L L

PY - 2016/1/7

Y1 - 2016/1/7

N2 - 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.

AB - 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.

KW - Fundamental Domain

KW - Subspace Versus

KW - Irrational Rotation

KW - Rational Subspace

U2 - 10.1007/s11856-016-1283-z

DO - 10.1007/s11856-016-1283-z

M3 - Article (Academic Journal)

SN - 0021-2172

VL - 212

SP - 189

EP - 201

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

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

Abstract

Keywords

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Projects

Diophantine approximation, chromatic number, and equivalence classes of separated nets

Career Acceleration Fellowship

Profiles

Dr Henna L L Koivusalo

Cite this