Constructing cut-and-project sets which are close to lattices
Alan Haynes, Henna Koivusalo · arXiv (Cornell University) · 2014
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.