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Real-expansive flows and topological dimension

Published online by Cambridge University Press:  19 September 2008

H. B. Keynes  and
M. Sears
H. B. Keynes*
Affiliation:
From the School of Mathematics, University of Minnesota, USA;
M. Sears
Affiliation:
Department of Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
*
†Address for correspondence: Dr H. B. Keynes, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

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We examine generalizations of R. Mañé's results on the topological dimension of spaces supporting an expansive homeomorphism to the case of real-expansive flows. We show that a space supporting a real-expansive flow must be finite dimensional, and a minimal real-expansive flow not exhibiting a type of spiral behaviour must be one-dimensional. This latter class includes all known examples and a slight generalization of Axiom A flows. These results are obtained by introducing a new concept of stable and unstable sets for real flows, and examining real-expansive flows in terms of these sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 2 , June 1981 , pp. 179 - 195
Copyright
Copyright © Cambridge University Press 1981

References

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