Time changes for R^<i>n</i>flows and suspensions

Abstract

We examine properties of flows on compact metric spaces under multi-parameter real actions (i.e., the acting group is R"), and the impact of changes of action (time changes) and conjugacies to other flows. These concepts are carefully studied in the case of R'-suspensions and a basic framework for the internal structure of suspensions is developed. The structure of minimal R" flows which are conjugate to an equicontinuous flow is examined using suspensions, and these flows are shown to be either weak-mixing or equicontinuous under suitable assumptions. Basic properties for the cohomology of time changes are also developed, with the major result indicating when time changes on equicontinuous minimal flows are cohomologous to constant time changes, and the structure of those time changes which themselves yield equicontinuous flows.