2024/02/26 by Sergey Bezuglyi, Bezuglyi, Sergey, Olena Karpel +3
Mathematics · #05C60 #37A05 #37A40 #37B05 #54H05 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2402.17046
openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] 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.