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 (x,t)↦(x+α,t+h(x)). 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.Comment: 31 page