QUASIFACTORS, PROXIMAL EXTENSIONS AND OTHER STRUCTURES OF NONDISCRETE MINIMAL FLOWS

Abstract. The classical theory of dynamical systems arose in the context of the study of differential 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 flows 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 compactification associated to the space of left norm continuous functions on S such that all minimal flows are flow isomorphic to quotients of this compactification. Furthermore we can associate a subgroup of the maximal group to each min-imal flow. In [7] a new topology is defined on this extended acting semigroup such that these associated subgroups are precisely the closed subgroups in this topology. Since these subgroups are of significant importance in tower constructions of flows, in this paper we will look at pertinent structural theorems in the context of this new topology. 1