A flow on a compact Hausdorff space 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. We study special classes of flows: periodic, cocyclic, and almost cocyclic, mainly in term of the possibility of extending this action continuously to various compactifications of the integers.
Keywords: flow on compact spaces, periodic and cocyclic flows, almost cocyclic flows
2000 MSC: 18B30,37C55,54C30,54B30
Theory and Applications of Categories, Vol. 25, 2011, No. 18, pp 490-507.