Journal article
Homeomorphic measures on stationary Bratteli diagrams
Journal of functional analysis, Vol.261(12), pp.3519-3548
12/15/2011
DOI: 10.1016/j.jfa.2011.08.009
Abstract
We study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation R. Equivalently, the set S is formed by ergodic probability measures invariant with respect to aperiodic substitution dynamical systems. The paper is devoted to the classification of measures mu from S with respect to a homeomorphism. The properties of the clopen values set (mu) are studied. It is shown that for every measure mu is an element of S there exists a subgroup G subset of R such that S(mu) = G boolean AND [0, 1]. A criterion of goodness is proved for such measures. Based on this result, the measures from S are classified up to a homeomorphism. We prove that for every good measure mu is an element of S there exist countably many measures {mu(i)}(i is an element of N) subset of S such that the measures mu and mu(i) are homeomorphic but the tail equivalence relations on the corresponding Bratteli diagrams are not orbit equivalent. (C) 2011 Elsevier Inc. All rights reserved.
Details
- Title: Subtitle
- Homeomorphic measures on stationary Bratteli diagrams
- Creators
- S Bezuglyi - Institute for Low Temperature Physics, 47 Lenin Avenue, 61103 Kharkov, UkraineO Karpel - Institute for Low Temperature Physics, 47 Lenin Avenue, 61103 Kharkov, Ukraine
- Resource Type
- Journal article
- Publication Details
- Journal of functional analysis, Vol.261(12), pp.3519-3548
- DOI
- 10.1016/j.jfa.2011.08.009
- ISSN
- 0022-1236
- eISSN
- 1096-0783
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Number of pages
- 30
- Grant note
- Akhiezer fund
- Language
- English
- Date published
- 12/15/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984240778002771
Metrics
12 Record Views