Work

Equivalence relations on separated nets arising from linear toral flows

Year: 2014

Type: article

Abstract: In 1998, Burago–Kleiner and McMullen independently proved the existence of separated nets in R d 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 R d -actions. We analyze the separated nets which arise via these constructions, focusing particularly on nets arising from linear R d -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.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms/pdu036

Authors: Alan Haynes, Michael Kelly, Barak Weiss

Institutions: University of York, The University of Texas at Austin, Tel Aviv University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: York University, Israel Science Foundation, Ben-Gurion University of the Negev, Engineering and Physical Sciences Research Council

Awards: G3132472811, G4784278714, G4838034796, G7220250192