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Assoc. Prof. Medynets

Research Interests

Ergodic Theory and Topological Dynamics, Orbit Equivalence,  Operator Algebras Associated to Dynamical Systems,    Tiling and Symbolic Dynamical Systems, Algebraic Properties of Transformation Groups, Representation Theory of Infinite Groups.

Preprints
  • On Virtual Conjugacy of Generalized Odometers (jointly with M.I. Cortez) (2015), download pdf.
  • Presentations of Topological Full Groups by Generators and Relations (jointly with R.I. Grigorchuk), download pdf
Publications
  • Second Order Ergodic Theorem for Self-Similar Tiling Systems (jointly with B. Solomyak), Ergodic Theory & Dynamical Systems34 (2014), no. 6, 2018-2053, download pdf.
  • On the algebraic properties of topological full groups (jointly with R. Grigorchuk).   Mat. Sb. 205 (2014), no. 6, 87 - 100. download pdf.
  • Finite Factor Representations of Higman-Thompson's groups (jointly with A. Dudko), Groups, Geometry, and Dynamics 8 (2014), no. 2, 375 - 389. download pdf.
  • On Characters of Inductive Limits of Symmetric Groups (jointly with A. Dudko),  Journal of Functional Analysis, 264 (2013), no. 7, 1565 - 1598. download pdf.
  • Finite Rank Bratteli diagrams: Structure of Invariant Measures (jointly with S. Bezuglyi, J. Kwiatkowski, and B. Solomyak) Transactions of the AMS365 (2013), no. 5, 2637 - 2679. download pdf.
  • Reconstruction of Orbits of Cantor Systems from Full Groups, Bulletin of the London Mathematical Society, Volume 43 Part 6 (2011), 1104–1110. This file slightly differs from the published version. download pdf
  • Invariant measures on stationary Bratteli diagrams (jointly with S. Bezuglyi, J. Kwiatkowski, and B. Solomyak). Ergodic Theory and Dynamical Systems, 30 (2010), no. 4, 973-1007. download pdf
  • Aperiodic substitution systems and their Bratteli diagrams (jointly with S. Bezuglyi and J. Kwiatkowski). Ergodic Theory and Dynamical Systems 29 (2009), no. 1, 37–72. download pdf
  • Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems (jointly with S. Bezuglyi). Colloquium Mathematicum 110 (2008), no. 2, 409–429. download pdf.
  • On approximation of homeomorphisms of a Cantor set. Fundamenta Mathematicae 194 (2007), no. 1, 1–13. download pdf.
  • Cantor aperiodic systems and Bratteli diagrams. Comptes Rendus Mathematique 342 (2006), no. 1, 43–46. download pdf.
  • Approximation in ergodic theory, Borel, and Cantor dynamics (jointly with S. Bezuglyi and J. Kwiatkowski). Algebraic and topological dynamics, 39–64, Contemporary Mathematics385download pdf.
  • The Rokhlin lemma for homeomorphisms of a Cantor set (jointly with S. Bezuglyi and A. H. Dooley). Proceedings of the American Mathematical Society 133 (2005), no. 10, 2957–2964.
  • Smooth automorphisms and path-connectedness in Borel dynamics (jointly with S. Bezuglyi). Indagationes Mathematicae 15 (2004), no. 4, 453–468.
Presentations
  1. Dynamics on Bratteli Diagrams. download pdf.
  2. The Second Order Ergodic Theorem for Substitution Tiling Systems. download pdf.
  3. Characters of Thompson's Group.  download pdf.
  4. Bratteli Diagrams for Aperiodic Systems. download pdf.
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