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

TY - JOUR

T1 - Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices

AU - Haynes, Alan

AU - Koivusalo, Henna Lotta Louisa

N1 - © 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.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

U2 - 10.1007/s11856-016-1283-z

DO - 10.1007/s11856-016-1283-z

M3 - Article

VL - 212

SP - 189

EP - 201

JO - Israel J. Math

JF - Israel J. Math

IS - 1

ER -