ON THE STRUCTURE OF MINIMAL R ⁿ ACTIONS

Abstract

In this paper we study several concepts and models which are relevant in describing both the topological and dynamical structure of a typical R ⁿ flow. Some of these ideas originated in our earlier papers, and those of other authors, and we here attempt to synthesise these concepts. We start with shear—a notion which describes how little equicontinuity the flow contains. We move to R ⁿ suspensions which depend on particular R ⁿ cocycles and easily obtain a crude representation of the flow as a tower—a partial suspension over a base flow which contains the shear. Rudolph's deep theory of suspension models is modified to provide a new suspension model which incorporates the shear as the base of the tower. Finally we investigate towers in the context of a special class of automorphisms to see when these objects are themselves suspensions.