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Skew products and minimal dynamical systems on separable Hilbert manifolds

Published online by Cambridge University Press:  19 September 2008

A. Fathi
A. Fathi
Affiliation:
G.R. 21 du CNRS, Université Paris-Sud, Bâtiment 425, F-91405 Orsay cedex, France
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Abstract

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We prove that any locally compact, non-compact, second countable group acts minimally on any metrizable connected manifold modelled on the separable Hilbert space.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 213 - 224
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Bessaga, C. & Pelczynski, A.. Selected Topics in Infinite Dimensional Topology. PWN: Warszawa (1975).Google Scholar
[2]Bourbaki, N.. Eléments de Mathématique, livre III, Topologie générale, chapitres 1 & 2, 4e édition. Herman: Paris (1965).Google Scholar
[3]Chapman, T. A.. Lectures on Hilbert Cube Manifolds. CBMS Regional Conference Series in Mathematics, number 28. Amer. Math. Soc: Providence (1976).CrossRefGoogle Scholar
[4]Ellis, R.. The construction of minimal discrete flows. Amer. J. of Math. 87 (1965), 564–574.CrossRefGoogle Scholar
[5]Fathi, A.. Existence de systèmes dynamiques minimaux sur I'espace de Hilbert séparable. Topology 22 (1983), 165–167.CrossRefGoogle Scholar
[6]Glasner, S. & Weiss, B.. On the construction of minimal skew products. Israel J. of Math. 34 (1979), 321–336.CrossRefGoogle Scholar
[7]Jones, R. & Parry, W.. Compact abelian group extensions of dynamical systems, II. Compositio Math. 25 (1972), 135–147.Google Scholar
[8]Mather, J.. Characterization of Anosov diffeomorphisms. Indag. Math. 30 (1968), 479–483.Google Scholar
[9]Rolewicz, S.. On orbits of elements. Studia Math. 32 (1969), 17–22.CrossRefGoogle Scholar
[10]West, J.. Extending certain transformation group actions in separable infinite dimensional Fréchet spaces and the Hilbert cube. Bull. Amer. Math. Soc. 74 (1968), 1015–1019.Google Scholar