Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Minimal sets in recurrent discrete flows

Author: Ronald A. Knight
Journal: Proc. Amer. Math. Soc. 100 (1987), 195-198
MSC: Primary 54H20
MathSciNet review: 883427
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54H20

Retrieve articles in all journals with MSC: 54H20

Additional Information

Keywords: Discrete flows, minimal set, recurrent
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society