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The structural stability of topological cocycles

Published online by Cambridge University Press:  01 October 1999

K. M. MADDEN ,
N. G. MARKLEY  and
M. SEARS
K. M. MADDEN
Affiliation:
Department of Mathematics and Computer Science, Drew University, Madison, NJ 07940, USA
N. G. MARKLEY
Affiliation:
Provost's Office, Alumni Memorial Building, Lehigh University, Bethlehem, PA 18015, USA
M. SEARS
Affiliation:
Department of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg 2050, South Africa
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Abstract

Cocycles of $Z^m$ actions on compact metric spaces can be used to construct $R^m$ actions or flows, called suspension flows. A suspension provides a higher-dimensional analog to the familiar flow under a function and we look to this construction as a way of generating interesting $R^m$ flows. Even more importantly, an $R^m$ flow with a free dense orbit has an almost one-to-one extension which is a suspension [6] and thus suspensions can be used to model general $R^m$ flows. In this paper we examine the sensitivity of the suspension construction to small perturbations in the cocycle. Theorem 4.7 establishes the fact that two cocycles that are sufficiently close yield suspensions that are isomorphic up to a time change.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 5 , October 1999 , pp. 1309 - 1324
Copyright
1999 Cambridge University Press

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