Kasjan S, Keller G, Lemańczyk M (2019)
Publication Language: English
Publication Type: Journal article, Online publication
Publication year: 2019
Book Volume: 2019
Pages Range: 2690-2734
Journal Issue: 9
URI: https://arxiv.org/abs/1702.02375
DOI: 10.1093/imrn/rnx196
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.
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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