Topological dynamics on nets
Topological dynamics on nets
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DOI：
10.1016/j.topol.2015.12.051
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发表时间：
2016-03
影响因子：
0.6
通讯作者：
V. Farmaki;D. Karageorgos;Andreas Koutsogiannis;A. Mitropoulos
中科院分区：
文献类型：
--
作者：
V. Farmaki;D. Karageorgos;Andreas Koutsogiannis;A. Mitropoulos
我们证明了递归和多个递归结果的拓扑动力系统的索引任意有向部分半群的上理想的基础，适合于这个半群，但在其他任意。然后将这些结果应用于具有数字表示的半群索引的拓扑动力系统。我们的理论包括递归和多重递归结果的拓扑动力系统，索引的自然数，或由有限的非空子集的自然数，证明了Furstenberg和韦斯，和类似的结果拓扑动力系统索引的话。
We prove recurrence and multiple recurrence results for topological dynamical systems indexed by an arbitrary directed partial semigroup with respect to a coideal basis suitable for this semigroup, but otherwise arbitrary. These results are then applied to topological dynamical systems indexed by semigroups possessing digital representation. Our theory includes recurrence and multiple recurrence results for topological dynamical systems, indexed by natural numbers, or by finite non-empty subsets of natural numbers, proved by Furstenberg and Weiss, and analogous results for topological dynamical systems indexed by words.