Auslander Systems

Abstract

The authors generalize the dynamical system constructed by J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved