Journal article
Inverse limit method for generalized Bratteli diagrams and invariant measures
Dissertationes Mathematicae, Vol.616, pp.1-80
09/23/2026
DOI: 10.4064/dm240529-23-2
Abstract
Generalized Bratteli diagrams with a countable set of vertices in every level are models for aperiodic Borel automorphisms. This paper is devoted to the description of all ergodic tail invariant probability measures on the path spaces of generalized Bratteli diagrams. Such measures can be identified with inverse limits of infinite-dimensional simplices associated with levels in generalized Bratteli diagrams. Though this method is general, we apply it to several classes of reducible generalized Bratteli diagrams. In particular, we explicitly describe all ergodic tail invariant probability measures for (i) the infinite Pascal graph and give the formulas for the values of such measures on cylinder sets, (ii) generalized Bratteli diagrams formed by a countable set of odometers, (iii) reducible generalized Bratteli diagrams with uncountable set of ergodic tail invariant probability measures. We also consider the method of measure extension by tail invariance from subdiagrams. We discuss the properties of the Vershik map defined on reducible generalized Bratteli diagrams.
Details
- Title: Subtitle
- Inverse limit method for generalized Bratteli diagrams and invariant measures
- Creators
- Sergey Bezuglyi - University of IowaOlena Karpel - AGH University of KrakowJan Kwiatkowski - Nicolaus Copernicus University
- Resource Type
- Journal article
- Publication Details
- Dissertationes Mathematicae, Vol.616, pp.1-80
- DOI
- 10.4064/dm240529-23-2
- ISSN
- 0012-3862
- eISSN
- 1730-6310
- Publisher
- POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
- Number of pages
- 80
- Grant note
- NCN (National Science Centre, Poland): 2019/35/D/ST1/01375 Program "Excellence Initiative - Research University" Polish Ministry of Science and Higher Education
O.K. is supported by the NCN (National Science Centre, Poland) Grant 2019/35/D/ST1/01375 and by the program "Excellence Initiative - Research University" for the AGH University of Krakow. O.K. is also partially supported by a subsidy from the Polish Ministry of Science and Higher Education for the AGH University of Krakow.
- Language
- English
- Date published
- 09/23/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985241008702771
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