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

Alan Haynes; Henna Koivusalo

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

Dynamical Systems 2014-11-12 v3 Number Theory

Authors: Alan Haynes , Henna Koivusalo

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.

Keywords

bounded remainder sets cut-and-project sets separated nets toral rotation Rauzy condition lattices

Cite

@article{arxiv.1402.2125,
  title  = {Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices},
  author = {Alan Haynes and Henna Koivusalo},
  journal= {arXiv preprint arXiv:1402.2125},
  year   = {2014}
}

Comments

11 pages, 1 figure, updated references, changed intro to give credit to a result of Liardet which we were previously unaware of

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

Abstract

Keywords

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