Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A MULTIPLE RECURRENCE THEOREM FOR COUNTABLE DIRECTED PARTIAL SEMIGROUP ACTIONS

  • Received : 2019.01.04
  • Accepted : 2019.04.25
  • Published : 2019.11.30
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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.

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References

  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
  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
  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
  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
  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