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Decisive Bratteli–Vershik models

Volume 247 / 2019

Tomasz Downarowicz, Olena Karpel Studia Mathematica 247 (2019), 251-271 MSC: Primary 37B05, 37B10; Secondary 54H20. DOI: 10.4064/sm170519-5-2 Published online: 9 November 2018


We focus on Bratteli–Vershik models of general compact zero-dimensional systems with the action of a homeomorphism. An ordered Bratteli diagram is called decisive if the corresponding Vershik map prolongs in a unique way to a homeomorphism of the whole path space of the Bratteli diagram. We prove that a compact invertible zero-dimensional system has a decisive Bratteli–Vershik model if and only if either the set of aperiodic points is dense, or its closure misses one periodic orbit.


  • Tomasz DownarowiczFaculty of Pure and Applied Mathematics
    Wrocław University of Science
    and Technology
    50-370 Wrocław, Poland
  • Olena KarpelB. Verkin Institute for
    Low Temperature Physics and Engineering
    National Academy of Sciences of Ukraine
    Kharkiv, Ukraine
    Department of Dynamical Systems
    Institute of Mathematics
    Polish Academy of Sciences
    51-617 Wrocław, Poland
    Current address:
    Faculty of Applied Mathematics
    AGH University of Science and Technology
    Al. Mickiewicza 30
    30-059 Kraków, Poland

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