Journal article
Subdiagrams and invariant measures on Bratteli diagrams
Ergodic theory and dynamical systems, Vol.37(8), pp.2417-2452
02/19/2015
DOI: 10.1017/etds.2016.8
Abstract
We study ergodic finite and infinite measures defined on the path space $X_B$ of a Bratteli diagram $B$ which are invariant with respect to the tail equivalence relation on $X_B$. Our interest is focused on measures supported by vertex and edge subdiagrams of $B$. We give several criteria when a finite invariant measure defined on the path space of a subdiagram of $B$ extends to a finite invariant measure on $B$. Given a finite ergodic measure on a Bratteli diagram $B$ and a subdiagram $B'$ of $B$, we find the necessary and sufficient conditions under which the measure of the path space $X_{B'}$ of $B'$ is positive. For a class of Bratteli diagrams of finite rank, we determine when they have maximal possible number of ergodic invariant measures. The case of diagrams of rank two is completely studied. We include also an example which explicitly illustrates the proved results.
Details
- Title: Subtitle
- Subdiagrams and invariant measures on Bratteli diagrams
- Creators
- M AdamskaS BezuglyiO KarpelJ Kwiatkowski
- Resource Type
- Journal article
- Publication Details
- Ergodic theory and dynamical systems, Vol.37(8), pp.2417-2452
- DOI
- 10.1017/etds.2016.8
- ISSN
- 1469-4417
- eISSN
- 1469-4417
- Language
- English
- Date published
- 02/19/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9983985710102771
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