On tame enveloping semigroups
| dc.creator | Glasner, Eli | |
| dc.date | 2004-06-27 | |
| dc.date | 2006-01-11 | |
| dc.date.accessioned | 2026-07-07T06:36:54Z | |
| dc.date.available | 2026-07-07T06:36:54Z | |
| dc.description | 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. | |
| dc.description | This update includes several corrections | |
| dc.identifier | https://arxiv.org/abs/math/0406549 | |
| dc.identifier | http://arxiv.org/abs/math/0406549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100239 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 54H20 | |
| dc.title | On tame enveloping semigroups | |
| dc.type | text |