Topological Dynamics

Examples: time flow for solutions of differential equations, symbolic dynamics, cellular automata, geodesic and horocyclic flows, interval exchange transformations, Chabauty space, profinite actions. Basic concepts: Factors and extensions, topological transitivity, minimality, equicontinutity, distality, proximality, weak mixing, almost 1-1 extenstions. Topological entropy. The Ellis semgroup, Ellis theorem on the existence of idempotents, Ellis-Auslander theorem, Hindeman?s theorem. Universal constructions. Stone Cech compactification. The universal ambit and the universal minimal flow. Universal proximal and strongly proximal flows. Furstenberg boundary.