The structural stability of topological cocycles

Cocycles of Z(m) actions on compact metric spaces can be used to construct Rm actions or flows, called suspension flows. A suspension provides a highe r-dimensional analog to the familiar flow under a function and we look to t his construction as a way of generating interesting Rm flows. Even more imp ortantly, an R-m flow with a free dense orbit has an almost one-to-one exte nsion which is a suspension [6] and thus suspensions can be used to model g eneral Rm hows. 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 t hat are isomorphic up to a time change.