Browse > Article
http://dx.doi.org/10.4134/BKMS.b190013

A MULTIPLE RECURRENCE THEOREM FOR COUNTABLE DIRECTED PARTIAL SEMIGROUP ACTIONS  

Zeng, Tiaoying (Department of Mathematics Shantou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.6, 2019 , pp. 1577-1588 More about this Journal
Abstract
We show a multiple recurrence theorem for topological dynamical systems with countable directed partial semigroup actions, which generalizes the well-know IP-version of multiple recurrence theorem proved by Furstenberg and Weiss.
Keywords
recurrence; multiple recurrent theorem; directed partial semigroup; coideal basis;
Citations & Related Records
연도 인용수 순위
  • Reference
1 V. Farmaki, D. Karageorgos, A. Koutsogiannis, and A. Mitropoulos, Topological dynamics on nets, Topology Appl. 201 (2016), 414-431. https://doi.org/10.1016/j.topol.2015.12.051   DOI
2 V. Farmaki and A. Koutsogiannis, Topological dynamics indexed by words, Topology Appl. 159 (2012), no. 7, 1678-1690. https://doi.org/10.1016/j.topol.2011.05.041   DOI
3 S. Ferri, N. Hindman and D. Strauss, Digital representation of semigroups and groups, Semigroup Forum 77 (2008), no. 1, 36-63. https://doi.org/10.1007/s00233-008-9074-4   DOI
4 H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, NJ, 1981.
5 H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61-85. https://doi.org/10.1007/BF02790008   DOI
6 N. Hindman, Finite sums from sequences within cells of a partition of N, J. Combinatorial Theory Ser. A 17 (1974), 1-11. https://doi.org/10.1016/0097-3165(74)90023-5   DOI