Horizontally stationary generalized Bratteli diagrams
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| author | Bezuglyi, Sergey Jorgensen, Palle E. T. Karpel, Olena Kwiatkowski, Jan |
| author_facet | Bezuglyi, Sergey Jorgensen, Palle E. T. Karpel, Olena Kwiatkowski, Jan |
| contents | Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Horizontally stationary generalized Bratteli diagrams Bezuglyi, Sergey Jorgensen, Palle E. T. Karpel, Olena Kwiatkowski, Jan Dynamical Systems 37A05, 37B05, 37A40, 54H05, 05C60 Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram. |
| title | Horizontally stationary generalized Bratteli diagrams |
| topic | Dynamical Systems 37A05, 37B05, 37A40, 54H05, 05C60 |
| url | https://arxiv.org/abs/2409.10084 |