Mathematics – Dynamical Systems
Scientific paper
2004-06-27
Mathematics
Dynamical Systems
This update includes several corrections
Scientific paper
A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of the Stone-Cech compactification of the natural numbers, or it is a "tame" topological space whose topology is determined by the convergence of sequences. In the latter case we say that the dynamical system is tame. We show that (i) a metric distal minimal system is tame iff it is equicontinuous (ii) for an abelian acting group a tame metric minimal system is PI (hence a weakly mixing minimal system is never tame), and (iii) a tame minimal cascade has zero topological entropy. We also show that for minimal distal-but-not-equicontinuous systems the canonical map from the enveloping operator semigroup onto the Ellis semigroup is never an isomorphism. This answers a long standing open question. We give a complete characterization of minimal systems whose enveloping semigroup is metrizable. In particular it follows that for abelian acting group such a system is equicontinuous.
No associations
LandOfFree
On tame enveloping semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On tame enveloping semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On tame enveloping semigroups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-281098