Measures and dynamics on Pascal-Bratteli diagrams
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916818748178432 |
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| author | Bezuglyi, Sergey Dudko, Artem Karpel, Olena |
| author_facet | Bezuglyi, Sergey Dudko, Artem Karpel, Olena |
| contents | We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams $B$ that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on $B$. For every probability tail invariant measure $ν_p$ on the classical Pascal-Bratteli diagram, we approximate the support of $ν_p$ by the path space of a subdiagram. By considering various orders on the edges of $B$, we define dynamical systems with various properties. We show that there exist orders such that the sets of infinite maximal and infinite minimal paths are empty. This implies that the corresponding Vershik map is a homeomorphism. We also describe orders on both $B$ and the classical Pascal-Bratteli diagram that generate either uncountably many minimal infinite and uncountably many maximal infinite paths, or uncountably many minimal infinite paths alongside countably infinitely many maximal infinite paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measures and dynamics on Pascal-Bratteli diagrams Bezuglyi, Sergey Dudko, Artem Karpel, Olena Dynamical Systems 37A05, 37B05, 37A40, 54H05, 28D05 We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams $B$ that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on $B$. For every probability tail invariant measure $ν_p$ on the classical Pascal-Bratteli diagram, we approximate the support of $ν_p$ by the path space of a subdiagram. By considering various orders on the edges of $B$, we define dynamical systems with various properties. We show that there exist orders such that the sets of infinite maximal and infinite minimal paths are empty. This implies that the corresponding Vershik map is a homeomorphism. We also describe orders on both $B$ and the classical Pascal-Bratteli diagram that generate either uncountably many minimal infinite and uncountably many maximal infinite paths, or uncountably many minimal infinite paths alongside countably infinitely many maximal infinite paths. |
| title | Measures and dynamics on Pascal-Bratteli diagrams |
| topic | Dynamical Systems 37A05, 37B05, 37A40, 54H05, 28D05 |
| url | https://arxiv.org/abs/2411.06280 |