Invariant measures on stationary Bratteli diagrams

S. Bezuglyi, J. Kwiatkowski, K. Medynets, B. Solomyak

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43 Scopus citations


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.

Original languageEnglish
Pages (from-to)973-1007
Number of pages35
JournalErgodic Theory and Dynamical Systems
Issue number4
StatePublished - Aug 2010
Externally publishedYes


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