Flows: cocyclic and almost cocyclic (Q2884467)

The paper studies flows from the point of view of the category theory. A flow is regarded as the category whose objects are pairs \((X,t)\) where \(X\) is a compact Hausdorff space and \(t:X\to X\) is an automorphism. Using the closed structure on the category of uniform spaces, a flow gives rise, by iteration, to an action of the integers on the topological group of automorphisms of the object. Mainly, the paper concerns special classes of flows: periodic, cocyclic, and almost cocyclic. These classes of flows are studied in term of the possibility of extending the action continuously to various compactifications of the integers.