Keller G, Richard C (2019)
Publication Language: English
Publication Type: Journal article
Publication year: 2019
Book Volume: 229
Pages Range: 85-132
Journal Issue: 1
DOI: 10.1007/s11856-018-1788-8
There is a renewed interest in weak model sets due to their connection to -free systems, which emerged from Sarnak's program on the M"obius disjointness conjecture. Here we continue our recent investigation [arXiv:1511.06137] of the extended hull GW, a dynamical system naturally associated to a weak model set in an abelian group G with relatively compact window W. For windows having a nowhere dense boundary (this includes compact windows), we identify the maximal equicontinuous factor of GW and give a sufficient condition when GW is an almost 1:1 extension of its maximal equicontinuous factor. If the window is measurable with positive Haar measure and is almost compact, then the system GW equipped with its Mirsky measure is isomorphic to its Kronecker factor. For general nontrivial ergodic probability measures on GW, we provide a kind of lower bound for the Kronecker factor. All relevant factor systems are natural G-actions on quotient subgroups of the torus underlying the weak model set. These are obtained by factoring out suitable window periods. Our results are specialised to the usual hull of the weak model set, and they are also interpreted for -free systems.
APA:
Keller, G., & Richard, C. (2019). Periods and factors of weak model sets. Israel Journal of Mathematics, 229(1), 85-132. https://dx.doi.org/10.1007/s11856-018-1788-8
MLA:
Keller, Gerhard, and Christoph Richard. "Periods and factors of weak model sets." Israel Journal of Mathematics 229.1 (2019): 85-132.
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