Topological dynamics on nets

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• 作者：Vassiliki Farmaki^a ; ^{vfarmaki@math.uoa.gr" class="auth_mail" title="E-mail the corresponding author} ; Dimitris Karageorgos^a ; ^{dimitris_kar@math.uoa.gr" class="auth_mail" title="E-mail the corresponding author} ; Andreas Koutsogiannis^b ; ^{koutsogiannis.1@osu.edu" class="auth_mail" title="E-mail the corresponding author} ; Andreas Mitropoulos^a ; ^{anmitrop@math.uoa.gr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 37Bxx ; secondary ; 54H20
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：201
• 期：Complete
• 页码：414-431
• 全文大小：441 K

文摘

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.