On Katznelson’s Question for skew-product systems
نویسندگان
چکیده
Katznelson’s Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to problems combinatorics harmonic analysis. In this article, we give positive answer for certain towers of skew-product extensions equicontinuous systems, including systems the form ( x , t stretchy="false">) stretchy="false">↦ + α h (x,t) \mapsto (x + \alpha , h(x)) . We describe which frequencies must be controlled order ensure such derive combinatorial corollaries difference sets syndetic subsets natural numbers.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2022
ISSN: ['0002-9904', '1936-881X']
DOI: https://doi.org/10.1090/bull/1764