Horizontally stationary generalized Bratteli diagrams

Sergey Bezuglyi; Palle E. T Jorgensen; Olena Karpel; Jan Kwiatkowski

doi:10.48550/arxiv.2409.10084

Back

Horizontally stationary generalized Bratteli diagrams

Preprint

Open access

Horizontally stationary generalized Bratteli diagrams

Sergey Bezuglyi, Palle E. T Jorgensen, Olena Karpel and Jan Kwiatkowski

ArXiv.org

09/16/2024

DOI: 10.48550/arxiv.2409.10084

Files and links (1)

url

https://doi.org/10.48550/arxiv.2409.10084View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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.

Mathematics - Dynamical Systems

Details

Title: Subtitle: Horizontally stationary generalized Bratteli diagrams
Creators: Sergey Bezuglyi
Palle E. T Jorgensen
Olena Karpel
Jan Kwiatkowski
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2409.10084
ISSN: 2331-8422
Language: English
Date posted: 09/16/2024
Academic Unit: Mathematics
Record Identifier: 9984704388502771

Metrics

61 Record Views