On Katznelson's Question for skew product systems
Abstract
Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to Katznelson's Question for certain towers of skew product extensions of equicontinuous systems, including systems of the form . We describe which frequencies must be controlled for in order to ensure recurrence in such systems, and we derive combinatorial corollaries concerning the difference sets of syndetic subsets of the natural numbers.
Keywords
Cite
@article{arxiv.2106.11393,
title = {On Katznelson's Question for skew product systems},
author = {Daniel Glasscock and Andreas Koutsogiannis and Florian K. Richter},
journal= {arXiv preprint arXiv:2106.11393},
year = {2023}
}
Comments
38 pages, revised version; the statement of Theorem C has become more general addressing the case in which a higher-order derivative of the sequence f is almost periodic. To appear in BAMS