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

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JournalIsrael J. Math
DateAccepted/In press - 17 Nov 2014
DateE-pub ahead of print - 7 Jan 2016
DatePublished (current) - 1 May 2016
Issue number1
Volume212
Number of pages13
Pages (from-to)189-201
Early online date7/01/16
Original languageEnglish

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.

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© 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.

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