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)



Regular PI metric flows are equicontinuous

Author: Eli Glasner
Journal: Proc. Amer. Math. Soc. 114 (1992), 269-277
MSC: Primary 54H20
MathSciNet review: 1070517
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ (X,T)$ be a metrizable minimal flow. We show that a homomorphism $ X\mathop \to \limits^\pi Y$, which is regular, and PI can be decomposed as $ X\mathop \to \limits^\sigma Z\mathop \to \limits^\rho Y,\pi = \rho \circ \sigma $, where $ \rho $ is proximal and $ \sigma $ is a compact group extension. In particular, assuming further that $ T$ is abelian and taking $ Y$ to be the trivial one point flow, we find that a metric regular PI flow is a compact group rotation.

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

  • [A] J. Auslander, Minimal flows and their extensions, North-Holland, Amsterdam, 1988. MR 956049 (89m:54050)
  • [B] S. Banach, Théorie des opérations linéaires, Chelsea, New York, 1963.
  • [E] R. Ellis, Lectures on topological dynamics, Benjamin, New York, 1969. MR 0267561 (42:2463)
  • [F] H. Furstenberg, The structure of distal flows, Amer. J. Math. 85 (1963), 477-515. MR 0157368 (28:602)
  • [Gl] S. Glasner, A topological version of a theorem of Veech and almost simple flows, Ergodic Theory Dynamical Systems 10, (1990), 463-482. MR 1074314 (92e:28012)
  • [G2] -, Proximal flows, Lecture Notes in Math., vol. 517, Springer-Verlag, New York, 1976. MR 0474243 (57:13890)
  • [Go] W. H. Gottschalk, Transitivity and equicontinuity, Bull. Amer. Math. Soc. 54 (1948), 982-984. MR 0026765 (10:199c)
  • [K] K. Kuratowski, Topology, vol. I., Warsaw 1948. MR 0217751 (36:840)
  • [N] I. Namioka, Ellis groups and compact right topological groups, Conference in Modern Analysis and Probability, Contemp. Math., vol. 26, Amer. Math. Soc., Providence, RI, 1984, pp. 295-300. MR 737409 (85j:54061)
  • [V] W. A. Veech, Topological dynamics, Bull. Amer. Math. Soc. 83 (1977), 775-830. MR 0467705 (57:7558)

Similar Articles

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

Retrieve articles in all journals with MSC: 54H20

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society