On the existence of ergodic automorphisms in ergodic ${\mathbb Z} ^d$-actions on compact groups
| dc.creator | Raja, C. R. E. | |
| dc.date | 2009-04-06 | |
| dc.date.accessioned | 2026-07-07T13:00:46Z | |
| dc.date.available | 2026-07-07T13:00:46Z | |
| dc.description | Let $K$ be a compact metrizable group and $\Ga$ be a finitely generated group of commuting automorphisms of $K$. We show that ergodicity of $\Ga$ implies $\Ga$ contains ergodic automorphisms if center of the action, $Z(\Ga) = \{\ap \in {\rm Aut}(K) \mid \ap {\rm commutes with elements of \rm} \Ga \}$ has DCC. To explain that the condition on the center of the action is not restrictive, we discuss certain abelian groups which in particular, retrieves Theorems of Berend \cite{Be} and Schmidt \cite{Sc1} proved in this context. | |
| dc.identifier | https://arxiv.org/abs/0904.0848 | |
| dc.identifier | http://arxiv.org/abs/0904.0848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225942 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Representation Theory | |
| dc.subject | 37A15; 37B05 | |
| dc.title | On the existence of ergodic automorphisms in ergodic ${\mathbb Z} ^d$-actions on compact groups | |
| dc.type | text |