Recurrence, rigidity, and popular differences
Dynamical Systems
2019-03-27 v3
Abstract
We construct a set such that every translate of 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.
Cite
@article{arxiv.1509.03901,
title = {Recurrence, rigidity, and popular differences},
author = {John T. Griesmer},
journal= {arXiv preprint arXiv:1509.03901},
year = {2019}
}
Comments
21 pages, comments welcome. Revision 3 fixes some typos, changes terminology to use "translate" where "shift" was used in previous versions