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Aperiodic substitution systems and their Bratteli diagrams

  • S. BEZUGLYI (a1), J. KWIATKOWSKI (a2) and K. MEDYNETS (a3)
  • DOI:
  • Published online: 01 February 2009

We study aperiodic substitution dynamical systems arising from non-primitive substitutions. We prove that the Vershik homeomorphism φ of a stationary ordered Bratteli diagram is topologically conjugate to an aperiodic substitution system if and only if no restriction of φ to a minimal component is conjugate to an odometer. We also show that every aperiodic substitution system generated by a substitution with nesting property is conjugate to the Vershik map of a stationary ordered Bratteli diagram. It is proved that every aperiodic substitution system is recognizable. The classes of m-primitive substitutions and derivative substitutions associated with them are studied. We discuss also the notion of expansiveness for Cantor dynamical systems of finite rank.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
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