Recurrence, rigidity, and popular differences

Abstract

We construct a set $S$ such that every translate of $S$ is a set of recurrence and a set of rigidity for a weak mixing measure preserving system. This construction generalizes or strengthens results of Katznelson, Saeki, Forrest, and Fayad and Kanigowski. The construction provides a density analogue of Julia Wolf's results on popular differences in finite abelian groups.

21 pages, comments welcome. Revision 3 fixes some typos, changes terminology to use "translate" where "shift" was used in previous versions

References in corpus (1)

• Bohr topology and difference sets for some abelian groups

Cited by in corpus (1)

• Rigidity, weak mixing, and recurrence in abelian groups