12 citations · 41 across the 34 of their papers we have counts for
32 papers · 1 filter
Generalized Bratteli diagrams without probability tail invariant measures
Andrew Barsky, Sergey Bezuglyi
The paper focuses on the following problem: given a generalized Bratteli diagram , determine conditions under which the tail equivalence relation does not admit a t…
Measures and dynamics on Pascal-Bratteli diagrams
Sergey Bezuglyi, Artem Dudko, Olena Karpel
We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams that are represented as the union of countably many classical Pascal-Bratteli…
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…
Measurable multiresolution systems, endomorphisms, and representations of Cuntz relations
Sergey Bezuglyi, Palle E. T. Jorgensen
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generaliz…
Bratteli diagrams in Borel dynamics
Sergey Bezuglyi, Palle E. T. Jorgensen, Olena Karpel +1
Bratteli-Vershik models have been very successfully applied to the study of various dynamical systems, in particular, in Cantor dynamics. In this paper, we study dynamics on the pa…
IFS measures on generalized Bratteli diagrams
Sergey Bezuglyi, Palle E. T. Jorgensen
The purpose of the paper is a general analysis of path space measures. Our focus is a certain path space analysis on generalized Bratteli diagrams. We use this in a systematic stud…
Substitution-dynamics and invariant measures for infinite alphabet-path space
Sergey Bezuglyi, Palle E. T. Jorgensen, Shrey Sanadhya
We study substitutions on countably infinite alphabet (without compactification) as Borel dynamical systems. We construct stationary and non-stationary generalized Bratteli-Vershik…
Harmonic analysis on graphs via Bratteli diagrams and path-space measures
Sergey Bezuglyi, Palle E. T. Jorgensen
The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov…
Cohomology of hyperfinite Borel actions
Sergey Bezuglyi, Shrey Sanadhya
We study cocycles of countable groups of Borel automorphisms of a standard Borel space taking values in a locally compact second countable group . We prov…
Invariant measures for Cantor dynamical systems
S. Bezuglyi, O. Karpel
This paper is a survey devoted to the study of probability and infinite ergodic invariant measures for aperiodic homeomorphisms of a Cantor set. We focus mostly on the cases when a…
Exact number of ergodic invariant measures for Bratteli diagrams
S. Bezuglyi, O. Karpel, J. Kwiatkowski
For a Bratteli diagram , we study the simplex of probability measures on the path space of which are invariant with respect to the tail equivalence relati…
Monopoles, dipoles, and harmonic functions on Bratteli diagrams
Sergey Bezuglyi, Palle E. T. Jorgensen
In our study of electrical networks we develop two themes: finding explicit formulas for special classes of functions defined on the vertices of a transient network, namely monopol…
Bratteli diagrams: structure, measures, dynamics
S. Bezuglyi, O. Karpel
This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space $X_…
Subdiagrams and invariant measures on Bratteli diagrams
M. Adamska, S. Bezuglyi, O. Karpel +1
We study ergodic finite and infinite measures defined on the path space of a Bratteli diagram which are invariant with respect to the tail equivalence relation on .…
Representations of Cuntz-Krieger relations, dynamics on Bratteli diagrams, and path-space measures
Sergey Bezuglyi, Palle E. T. Jorgensen
We study a new class of representations of the Cuntz-Krieger algebras constructed by semibranching function systems, naturally related to stationary Bratteli diagram…
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…
Perfect orderings on Bratteli diagrams II: general Bratteli diagrams
Sergey Bezuglyi, Reem Yassawi
We continue our study of orderings on Bratteli diagrams started in previous work, joint with Jan Kwiatkowski, where Bratteli diagrams of finite rank were considered. We extend the…
Perfect orderings on Bratteli diagrams
Sergey Bezuglyi, Jan Kwiatkowski, Reem Yassawi
Given a Bratteli diagram B, we study the set O(B) of all possible orderings w on a Bratteli diagram B and its subset P(B) consisting of `perfect' orderings that produce Bratteli-Ve…
Measures on Cantor sets: the good, the ugly, the bad
Sergey Bezuglyi, David Handelman
We translate Akin's notion of {\it good} (and related concepts) from measures on Cantor sets to traces on dimension groups, and particularly for invariant measures of minimal homeo…
Orbit equivalent substitution dynamical systems and complexity
S. Bezuglyi, O. Karpel
For any primitive proper substitution σ, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X_{ζ_n}, T_{ζ_n})}_{n=1}^{\infty}…
Homeomorphic measures on stationary Bratteli diagrams
S. Bezuglyi, O. Karpel
We study the set S of ergodic probability Borel measures on stationary non-simple Bratteli diagrams which are invariant with respect to the tail equivalence relation. Equivalently,…
Finite Rank Bratteli Diagrams: Structure of Invariant Measures
Sergey Bezuglyi, Jan Kwiatkowski, Konstantin Medynets +1
We consider Bratteli diagrams of finite rank (not necessarily simple) and ergodic invariant measures with respect to the cofinal equivalence relation on their path spaces. It is sh…