Geodesic
Subdiagrams of Bratteli Diagrams Supporting Finite Invariant Measures
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 3-17 
S. Bezuglyi; O. Karpel; J. Kwiatkowski. Subdiagrams of Bratteli Diagrams Supporting Finite Invariant Measures. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2015) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/JMAG_2015_11_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study finite measures on Bratteli diagrams invariant with respect to the tail equivalence relation. Amongst the proved results on the finiteness of measure extension, we characterize the vertices of a Bratteli diagram that support an ergodic finite invariant measure.

[1] S. Bezuglyi, J. Kwiatkowski, K. Medynets, B. Solomyak, “Invariant Measures on Stationary Bratteli Diagrams”, Ergodic Theory Dynam. Syst., 30 (2013), 973–1007 | DOI | MR

[2] S. Bezuglyi, O. Karpel, “Homeomorphic Measures on Stationary Bratteli Diagrams”, J. Funct. Anal., 261 (2011), 3519–3548 | DOI | MR | Zbl

[3] S. Bezuglyi, J. Kwiatkowski, K. Medynets, B. Solomyak, “Finite Rank Bratteli Diagrams: Structure of Invariant Measures”, Trans. Amer. Math. Soc., 365 (2013), 2637–2679 | DOI | MR | Zbl

[4] S. Bezuglyi, J. Kwiatkowski, R. Yassawi, “Perfect Orderings on Finite Rank Bratteli Diagrams”, Canad. J. Math., 66 (2014), 57–101 | DOI | MR | Zbl

[5] S. Bezuglyi, R. Yassawi, Perfect Orderings on General Bratteli Diagrams, Preprint, 2013

[6] F. Durand, “Combinatorics on Bratteli Diagrams and Dynamical Systems”, Combinatorics, Automata and Number Theory, Encyclopedia of Mathematics and its Applications, 135, eds. V. Berthé, M. Rigo, Cambridge University Press, 2010, 338–386 | MR

[7] T. Giordano, I. Putnam, C. Skau, “Topological Orbit Equivalence and $C^*$-Crossed Products”, J. Reine Angew. Math., 469 (1995), 51–111 | MR | Zbl

[8] R. H. Herman, I. Putnam, C. Skau, “Ordered {Bratteli} Diagrams, Dimension Groups, and Topological Dynamics”, Int. J. Math., 3:6 (1992), 827–864 | DOI | MR | Zbl

[9] K. Medynets, “Cantor Aperiodic Systems and Bratteli Diagrams”, C. R., Acad. Sci. Paris, Ser. 1, 342 (2006), 43–46 | DOI | MR