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Proceedings of the American Mathematical Society

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Minimal sets in recurrent discrete flows


Author: Ronald A. Knight
Journal: Proc. Amer. Math. Soc. 100 (1987), 195-198
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1987-0883427-7
MathSciNet review: 883427
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Abstract: Each orbit closure of a recurrent discrete flow on a locally compact space is shown to contain at most one compact minimal subset. In particular, such an orbit closure contains a unique compact minimal subset if and only if the orbit closure is compact.


References [Enhancements On Off] (What's this?)

  • [1] Y. Katznelson and B. Weiss, When all points are recurrent/generic, Ergodic Theory and Dynamical Systems. I, Birkhäuser, Boston-Basel-Stuttgart, 1981, pp. 195-210. MR 633765 (83b:54056)
  • [2] R. Knight, Prolongationally stable discrete flows, Fund. Math. 108 (1980), 137-144. MR 594313 (82e:54047)
  • [3] -, Compact discrete flows, Fund. Math. 118 (1983), 193-190. MR 736278 (85c:54071)
  • [4] -, A characterization of recurrent motions, Bull. Austral. Math. Soc. 28 (1983), 1-4. MR 726796 (85f:54090)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0883427-7
Keywords: Discrete flows, minimal set, recurrent
Article copyright: © Copyright 1987 American Mathematical Society

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