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Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices
Research output: Contribution to journal › Article › peer-review
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Publication details
| Journal | Israel J. Math |
|---|---|
| Date | Accepted/In press - 17 Nov 2014 |
| Date | E-pub ahead of print - 7 Jan 2016 |
| Date | Published (current) - 1 May 2016 |
| Issue number | 1 |
| Volume | 212 |
| Number of pages | 13 |
| Pages (from-to) | 189-201 |
| Early online date | 7/01/16 |
| Original language | English |
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.
Research supported by EPSRC grants EP/J00149X/1 and EP/L001462/1.
Research supported by EPSRC grants EP/J00149X/1 and EP/L001462/1.
Bibliographical note
© Hebrew University of Jerusalem 2016. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Projects
Career Acceleration Fellowship: Circle rotations and their generalisation in Diophantine approximation
Project: Research project (funded) › Research
Diophantine approximation, chromatic number, and equivalence classes of separated nets
Project: Research project (funded) › Research
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