Journal article
Invariant measures on stationary Bratteli diagrams
Ergodic theory and dynamical systems, Vol.30(4), pp.973-1007
08/01/2010
DOI: 10.1017/S0143385709000443
Abstract
We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we give an explicit description of all ergodic probability measures that are invariant with respect to the tail equivalence relation (or the Vershik map); these measures are completely described by the incidence matrix of the Bratteli diagram. Since such diagrams correspond to substitution dynamical systems, our description provides an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.
Details
- Title: Subtitle
- Invariant measures on stationary Bratteli diagrams
- Creators
- S Bezuglyi - †Institute for Low Temperature Physics, 47 Lenin Avenue, 61103 Kharkov, Ukraine (J Kwiatkowski - ‡College of Economics and Computer Sciences, Barczewskiego 11, 10106 Olsztyn, Poland (K Medynets - †Institute for Low Temperature Physics, 47 Lenin Avenue, 61103 Kharkov, Ukraine (B Solomyak - University of Washington
- Resource Type
- Journal article
- Publication Details
- Ergodic theory and dynamical systems, Vol.30(4), pp.973-1007
- DOI
- 10.1017/S0143385709000443
- ISSN
- 0143-3857
- eISSN
- 1469-4417
- Publisher
- CAMBRIDGE UNIV PRESS
- Number of pages
- 35
- Grant note
- 05-109-53-15 / INTAS YSF NN201384834 / MNiSzW Akhiezer fund DMS-0355187; DMS-0654408 / NSF
- Language
- English
- Date published
- 08/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984241045402771
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