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Invariant Measures for Reducible Generalized Bratteli Diagrams
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Invariant Measures for Reducible Generalized Bratteli Diagrams

Sergey Bezuglyi, Olena Karpel and Jan Kwiatkowski
Journal of mathematical physics, analysis, geometry, Vol.20(1), pp.3-24
01/01/2024
DOI: 10.15407/mag20.01.003

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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.
Mathematics Physical Sciences Physics Mathematics, Applied Physics, Mathematical Science & Technology

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