5 papers
Horizontally stationary generalized Bratteli diagrams
Sergey Bezuglyi, Palle E. T. Jorgensen, Olena Karpel +1
Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli dia…
Inverse limit method for generalized Bratteli diagrams and invariant measures
Sergey Bezuglyi, Olena Karpel, Jan Kwiatkowski +1
Generalized Bratteli diagrams with a countable set of vertices in every level are models for aperiodic Borel automorphisms. This paper is devoted to the description of all ergodic…
Invariant measures for reducible generalized Bratteli diagrams
Sergey Bezuglyi, Olena Karpel, Jan Kwiatkowski
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…
Subdiagrams of Bratteli diagrams supporting finite invariant measures
S. Bezuglyi, O. Karpel, J. Kwiatkowski
We study finite measures on Bratteli diagrams invariant with respect to the tail equivalence relation. Amongst the proved results on finiteness of measure extension, we characteriz…
Approximation in ergodic theory, Borel, and Cantor dynamics
S. Bezuglyi, J. Kwiatkowski, K. Medynets
This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density,…