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arXiv · 1501.01491

Multi-recurrence and van der Waerden systems

Dominik Kwietniak·Jian Li·Piotr Oprocha·Xiangdong Ye
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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.

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Dominik Kwietniak, Jian Li, Piotr Oprocha, Xiangdong Ye. 2015-01-07. Multi-recurrence and van der Waerden systems. https://doi.org/10.1007/s11425-015-0860-8

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