Preprint
Measures and dynamics on Pascal-Bratteli diagrams
ArXiv.org
Cornell University
07/01/2025
DOI: 10.48550/arxiv.2411.06280
Abstract
We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on . For every probability tail invariant measure on the classical Pascal-Bratteli diagram, we approximate the support of by the path space of a subdiagram. By considering various orders on the edges of , 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 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.
Details
- Title: Subtitle
- Measures and dynamics on Pascal-Bratteli diagrams
- Creators
- Sergey BezuglyiArtem DudkoOlena Karpel
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2411.06280
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 07/01/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984936609202771
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