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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

Abstract

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.

Authors

  • Tomasz DownarowiczFaculty of Pure and Applied Mathematics
    Wrocław University of Science
    and Technology
    50-370 Wrocław, Poland
    e-mail
  • Olena KarpelB. Verkin Institute for
    Low Temperature Physics and Engineering
    National Academy of Sciences of Ukraine
    Kharkiv, Ukraine
    and
    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
    e-mail

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