Topological Dynamics and Semigroup Compactifications
by
Jimmie Lawson
Louisiana State University

In this talk we survey the role of semigroup compactifications in topological dynamics, where the dynamical systems (or flows) considered consist of the continuous action of a topological group G (or semigroup) on a compact phase space X. One can extend the action to a compact semigroup, called the Ellis or enveloping semigroup compactification, which is obtained by taking the pointwise closure of G in X^X. Various properties of the flow, particularly for minimal flows, such as distality, proximality, and almost periodicity can be fruitfully studied via properties and structure of the Ellis semigroup, particularly the structure of its minimal ideal. The machinery of the Ellis semigroup allows one to bring algebraic ideas and techniques to bear for the study of topological properties of the flow.

Date received: February 11, 2000