Dynamics of B-Free sets: a view through the window

Kasjan S, Keller G, Lemańczyk M (2019)

Publication Language: English

Publication Type: Journal article, Online publication

Publication year: 2019

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Book Volume: 2019

Pages Range: 2690-2734

Journal Issue: 9

URI: https://arxiv.org/abs/1702.02375

DOI: 10.1093/imrn/rnx196

Abstract

Let  be an infinite subset of {1,2,…}. We characterize arithmetic and dynamical properties of the -free set  through group theoretical, topological and measure theoretic properties of a set W (called the window) associated with . This point of view stems from the interpretation of the set  as a weak model set. Our main results are:  is taut if and only if the window is Haar regular; the dynamical system associated to  is a Toeplitz system if and only if the window is topologically regular; the dynamical system associated to  is proximal if and only if the window has empty interior; and the dynamical system associated to  has the "na"ively expected" maximal equicontinuous factor if and only if the interior of the window is aperiodic.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Nicolaus Copernicus University (NCU) / Uniwersytet Mikołaja Kopernika w Toruniu (UMK) PL Poland (PL)

How to cite

APA:

Kasjan, S., Keller, G., & Lemańczyk, M. (2019). Dynamics of B-Free sets: a view through the window. International Mathematics Research Notices, 2019(9), 2690-2734. https://dx.doi.org/10.1093/imrn/rnx196

MLA:

Kasjan, Stanislaw, Gerhard Keller, and Mariusz Lemańczyk. "Dynamics of B-Free sets: a view through the window." International Mathematics Research Notices 2019.9 (2019): 2690-2734.

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