Journal article
Exact number of ergodic invariant measures for Bratteli diagrams
Journal of mathematical analysis and applications, Vol.480(2), p.123431
12/15/2019
DOI: 10.1016/j.jmaa.2019.123431
Abstract
For a Bratteli diagram B, we study the simplex M1(B) of probability measures on the path space of B which are invariant with respect to the tail equivalence relation. Equivalently, M1(B) is formed by probability measures invariant with respect to a homeomorphism of a Cantor set. We study relations between the number of ergodic measures from M1(B) and the structure and properties of the diagram B. We prove a criterion and find sufficient conditions of unique ergodicity of a Bratteli diagram, in which case the simplex M1(B) is a singleton. For a finite rank k Bratteli diagram B having exactly l≤k ergodic invariant measures, we explicitly describe the structure of the diagram and find the subdiagrams which support these measures. We find sufficient conditions under which: (i) a Bratteli diagram has a prescribed number (finite or infinite) of ergodic invariant measures, and (ii) the extension of a measure from a uniquely ergodic subdiagram gives a finite ergodic invariant measure. Several examples, including stationary Bratteli diagrams, Pascal-Bratteli diagrams, and Toeplitz flows, are considered.
Details
- Title: Subtitle
- Exact number of ergodic invariant measures for Bratteli diagrams
- Creators
- Sergey Bezuglyi - University of IowaOlena Karpel - AGH University of KrakowJan Kwiatkowski - 3F
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.480(2), p.123431
- Publisher
- Elsevier Inc
- DOI
- 10.1016/j.jmaa.2019.123431
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Grant note
- name: NAS of Ukraine, award: 0119U102376; DOI: 10.13039/501100004281, name: NCN, award: 2013/08/A/ST1/00275; name: Nicolas Copernicus University; DOI: 10.13039/100008893, name: University of Iowa
- Language
- English
- Date published
- 12/15/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984240862502771
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