Sergii Bezuglyi, Ph.D.

Generalized Bratteli diagrams are models for aperiodic Borel automorphisms of standard Borel spaces. To describe all probability tail invariant measures on the path spaces of a generalized Bratteli diagram, we use the inverse limit method applied to infinite-dimensional simplices associated with levels in generalized Bratteli diagrams. In particular, we explicitly describe all ergodic tail invariant probability measures for (i) the infinite Pascal graph and give the formulas for the values of such measures on cylinder sets, (ii) generalized Bratteli diagrams formed by a countable set of odometers, (iii) reducible generalized Bratteli diagrams with uncountable set of ergodic tail invariant probability measures.
The talk is based on a joint paper with O. Karpel, J. Kwiatkowski, M. Wata.

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