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

Alan Haynes; Michael Kelly; Henna Koivusalo

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

Dynamical Systems 2016-02-02 v1 Number Theory

Authors: Alan Haynes , Michael Kelly , Henna Koivusalo

Abstract

Recent results of several authors have led to constructions of parallelotopes which are bounded remainder sets for totally irrational toral rotations. In this brief note we explain, in retrospect, how some of these results can easily be obtained from a geometric argument which was previously employed by Duneau and Oguey in the study of deformation properties of mathematical models for quasicrystals.

Keywords

bounded remainder sets cut-and-project sets lattices toral rotations quasicrystals parallelotopes geometric argument

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@article{arxiv.1602.00529,
  title  = {Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices, II},
  author = {Alan Haynes and Michael Kelly and Henna Koivusalo},
  journal= {arXiv preprint arXiv:1602.00529},
  year   = {2016}
}

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9 pages

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

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