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

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 languageEnglish
Pages (from-to)189-201
JournalIsrael Journal of Mathematics
Volume212
DOIs
Publication statusPublished - 7 Jan 2016

Keywords

  • Fundamental Domain
  • Subspace Versus
  • Irrational Rotation
  • Rational Subspace

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