@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",

}