Multi-recurrence and van der Waerden systems
Dynamical Systems
2016-12-28 v3 Combinatorics
Abstract
We explore recurrence properties arising from dynamical approach to combinatorial problems like the van der Waerden Theorem. We describe relations between these properties, study their consequences for dynamics, and demonstrate connections to combinatorial problems. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity in topological weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.
Cite
@article{arxiv.1501.01491,
title = {Multi-recurrence and van der Waerden systems},
author = {Dominik Kwietniak and Jian Li and Piotr Oprocha and Xiangdong Ye},
journal= {arXiv preprint arXiv:1501.01491},
year = {2016}
}
Comments
29 pages. Small changes during the proofing stage