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Flows and compactifications. (English) Zbl 0769.54045
Some of the basic relationships between $$S$$-flows and monoidal compactifications of the topological semigroup $$S$$ are established and then this machinery is used for the study of flows. It is shown that many standard types of $$S$$-flows (such as proximal, distal or aperiodic) can be characterized by natural restrictions on the minimal ideal of the Ellis or enveloping semigroup of the flow. Using these characterizations properties of these flows are studied. It is also shown that some flows universal with respect to some property turn out to carry in a natural way a semigroup structure which sometimes allows one to establish additional properties of the flow.

##### MSC:
 54H20 Topological dynamics (MSC2010)
##### Keywords:
topological semigroup; flow
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