Invariant measures for reducible generalized Bratteli diagrams
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910345227927552 |
|---|---|
| author | Bezuglyi, Sergey Karpel, Olena Kwiatkowski, Jan |
| author_facet | Bezuglyi, Sergey Karpel, Olena Kwiatkowski, Jan |
| contents | In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non-stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17046 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant measures for reducible generalized Bratteli diagrams Bezuglyi, Sergey Karpel, Olena Kwiatkowski, Jan Dynamical Systems 37A05, 37B05, 37A40, 54H05, 05C60 In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non-stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik homeomorphism. |
| title | Invariant measures for reducible generalized Bratteli diagrams |
| topic | Dynamical Systems 37A05, 37B05, 37A40, 54H05, 05C60 |
| url | https://arxiv.org/abs/2402.17046 |