Structures on the Isotropy Groups of Minimal Flows

The classical theory of dynamical systems arose in the context of the study of di erential equations. In recent years the study of these systems has been extended beyond discrete or continuous (real) phase groups or semigroups to the theory of ows of more general topological groups or semigroups. Let S be a semitopological semigroup, not necessarily discrete. An action of S on a compact phase space can then be extended to a compacti cation associated to the space of left norm continuous functions on S such that all minimal ows are ow isomorphic to quotients of this compacti cation. Furthermore we can associate a subgroup of the maximal group to each minimal ow. In [7] a new topology is de ned on this extended acting semigroup such that these associated subgroups are precisely the closed subgroups in this topology. Since these subgroups are of signi cant importance in tower constructions of ows, in this paper we will look at pertinent structural thorems in the context of this new topology.