We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynam...We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.展开更多
基金supported by the National Science Centre (Grant No. DEC-2012/07/E/ ST1/00185)National Natural Science Foundation of China (Grant Nos. 11401362, 11471125, 11326135, 11371339 and 11431012)+1 种基金Shantou University Scientific Research Foundation for Talents (Grant No. NTF12021)the Project of LQ1602 IT4Innovations Excellence in Science
文摘We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.
