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Multi-recurrence and van der Waerden systems |
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| Authors: | Dominik Kwietniak Jian Li Piotr Oprocha XiangDong Ye |
| Affiliation: | 1.Faculty of Mathematics and Computer Science,Jagiellonian University in Kraków,Kraków,Poland;2.Department of Mathematics,Shantou University,Shantou,China;3.Faculty of Applied Mathematics,AGH University of Science and Technology,Kraków,Poland;4.National Supercomputing Centre IT4Innovations, Division of the University of Ostrava, Institute for Research and Applications of Fuzzy Modeling,University of Ostrava,Ostrava,Czech Republic;5.Wu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences,University of Science and Technology of China,Hefei,China |
| Abstract: | 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. |
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