Invariant Measures on Stationary Bratteli Diagrams

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

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Pages (from-to)2637-2679
JournalTransactions of the American Mathematical Society
Issue number4
StatePublished - 2009


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