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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of York Heslington, York, YO10 5DD, UK

    Alan Haynes & Henna Koivusalo

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  1. Alan Haynes
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  2. Henna Koivusalo
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Correspondence to Henna Koivusalo.

Additional information

Research supported by EPSRC grants EP/J00149X/1 and EP/L001462/1.

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Haynes, A., Koivusalo, H. Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices. Isr. J. Math. 212, 189–201 (2016). https://doi.org/10.1007/s11856-016-1283-z

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  • DOI: https://doi.org/10.1007/s11856-016-1283-z

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