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)



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
Full-text PDF Free Access

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] H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, Princeton University Press, Princeton, N.J., 1981. M. B. Porter Lectures. MR 603625
  • [2] H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61–85 (1979). MR 531271,
  • [3] S. Glasner, Divisible properties and the Stone-Čech compactification, Canad. J. Math. 32 (1980), no. 4, 993–1007. MR 590662,
  • [4] Gottschalk, W. H., and Hedlund, G. A., Topological Dynamics, AMS Colloquium Publications, 36, 1955 MR 17:650e
  • [5] Neil Hindman, Finite sums from sequences within cells of a partition of 𝑁, J. Combinatorial Theory Ser. A 17 (1974), 1–11. MR 0349574
  • [6] Neil Hindman, Ultrafilters and combinatorial number theory, Number theory, Carbondale 1979 (Proc. Southern Illinois Conf., Southern Illinois Univ., Carbondale, Ill., 1979) Lecture Notes in Math., vol. 751, Springer, Berlin, 1979, pp. 119–184. MR 564927
  • [7] van der Waerden, B., Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212-216

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 37B20

Retrieve articles in all journals with MSC (2000): 37B20

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