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Sets that force recurrence

Authors: Alexander Blokh and Adam Fieldsteel
Journal: Proc. Amer. Math. Soc. 130 (2002), 3571-3578
MSC (2000): Primary 37B20
Published electronically: July 15, 2002
MathSciNet review: 1920036
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Abstract | References | Similar Articles | Additional Information

Abstract: We characterize those subsets $S$ of the positive integers with the property that, whenever a point $x$ in a dynamical system enters a compact set $K$along $S$, $K$ contains a recurrent point. We do the same for uniform recurrence.

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

  • [1] Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, NJ, 1981 MR 82j:28010
  • [2] Furstenberg, H. and Weiss, B., Topological dynamics and combinatorial number theory, J. D'Analyse Math, 34 (1978), pp. 61-85 MR 80g:05009
  • [3] Glasner, S., Divisible properties and the Stone-Cech compactification, Can. J. Math., 34, No. 4, 1980, pp. 993-1007 MR 82a:54040
  • [4] Gottschalk, W. H., and Hedlund, G. A., Topological Dynamics, AMS Colloquium Publications, 36, 1955 MR 17:650e
  • [5] Hindman, N., Finite sums from sequences within cells of a partition of N, J. Combin. Th., A17 (1974), 1-11 MR 50:2067
  • [6] Hindman, N., Ultrafilters and combinatorial number theory, Number Theory Carbondale 1979, M. Nathanson, ed., Lecture Notes in Math., 751 (1979), 119-184 MR 81m:10019
  • [7] van der Waerden, B., Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212-216

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Additional Information

Alexander Blokh
Affiliation: Department of Mathematics, University of Alabama at Birmingham, UAB Station, Birmingham, Alabama 35294-2060

Adam Fieldsteel
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459

Received by editor(s): November 30, 2000
Published electronically: July 15, 2002
Additional Notes: The first author was partially supported by NSF grant DMS-9970363
Communicated by: Michael Handel
Article copyright: © Copyright 2002 American Mathematical Society

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