Journal article
Invariant Measures for Reducible Generalized Bratteli Diagrams
Journal of mathematical physics, analysis, geometry, Vol.20(1), pp.3-24
01/01/2024
DOI: 10.15407/mag20.01.003
Abstract
In 2010, Bezuglyi, Kwiatkowski, Medynets, and Solomyak [10] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non -stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik homeomorphism.
Details
- Title: Subtitle
- Invariant Measures for Reducible Generalized Bratteli Diagrams
- Creators
- Sergey Bezuglyi - Univ Iowa, Dept Math, Iowa City, IA 52242 USAOlena Karpel - AGH University of KrakowJan Kwiatkowski - Nicolaus Copernicus University
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical physics, analysis, geometry, Vol.20(1), pp.3-24
- DOI
- 10.15407/mag20.01.003
- ISSN
- 1812-9471
- eISSN
- 1817-5805
- Publisher
- B VERKIN INST LOW TEMPERATURE PHYSICS & ENGINEERING NAS UKRAINE
- Number of pages
- 22
- Grant note
- Program "Excellence initiative - research university" Nicolas Copernicus University in Torun 2019/35/D/ST1/01375 / NCN (National Science Center, Poland)
- Language
- English
- Date published
- 01/01/2024
- Academic Unit
- Mathematics
- Record Identifier
- 9984936609502771
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