Aperiodic substitutional systems and their Bratteli diagrams
| dc.creator | Bezuglyi, S. | |
| dc.creator | Kwiatkowski, J. | |
| dc.creator | Medynets, K. | |
| dc.date | 2007-05-28 | |
| dc.date.accessioned | 2026-07-07T08:03:25Z | |
| dc.date.available | 2026-07-07T08:03:25Z | |
| dc.description | In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism $ϕ$ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional system if and only if no restriction of $ϕ$ to a minimal component is homeomorphic to an odometer. We also show that every aperiodic substitutional system generated by a substitution with nesting property is homeomorphic to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitutional system is recognizable. The classes of $m$-primitive substitutions and associated to them derivative substitutions are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank. | |
| dc.description | 42 pages | |
| dc.identifier | https://arxiv.org/abs/0705.4080 | |
| dc.identifier | http://arxiv.org/abs/0705.4080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129575 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37B10; 37B05 | |
| dc.title | Aperiodic substitutional systems and their Bratteli diagrams | |
| dc.type | text |