@article{353f084042bf401b8da7625e10863888,
title = "Equivalence relations on separated nets arising from linear toral flows",
abstract = "In 1998, Burago-Kleiner and McMullen independently proved the existence of separated nets in ℝd which are not bi-Lipschitz equivalent (BL) to a lattice. A finer equivalence relation than BL is bounded displacement (BD). Separated nets arise naturally as return times to a section for minimal ℝd-actions. We analyze the separated nets which arise via these constructions, focusing particularly on nets arising from linear ℝd-actions on tori. We show that generically these nets are BL to a lattice, and for some choices of dimensions and sections, they are generically BD to a lattice. We also show the existence of such nets which are not BD to a lattice.",
author = "Alan Haynes and Michael Kelly and Barak Weiss",
note = "Publisher Copyright: {\textcopyright} 2014 London Mathematical Society.",
year = "2013",
month = may,
day = "9",
doi = "10.1112/plms/pdu036",
language = "אנגלית",
volume = "109",
pages = "1203--1228",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "John Wiley and Sons Ltd",
number = "5",
}