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Constructive symbolic presentations of rank one measure-preserving systems

Volume 150 / 2017

Terrence Adams, Sébastien Ferenczi, Karl Petersen Colloquium Mathematicum 150 (2017), 243-255 MSC: Primary 37A05, 37B10, 28D05. DOI: 10.4064/cm7124-3-2017 Published online: 10 August 2017


Given a rank one measure-preserving system defined by cutting and stacking with spacers, we produce a rank one binary sequence such that its orbit closure under the shift transformation, with its unique nonatomic invariant probability, is isomorphic to the given system. In particular, the classical dyadic odometer is presented in terms of a recursive sequence of blocks on the two-symbol alphabet $\{0,1\}$. The construction is accomplished using a definition of rank one in the setting of adic, or Bratteli–Vershik, systems.


  • Terrence AdamsU.S. Government
    9800 Savage Rd
    Ft. Meade, MD 20755, U.S.A.
  • Sébastien FerencziAix Marseille Université
    CNRS, Centrale Marseille
    Institut de Mathématiques de Marseille
    I2M–UMR 7373
    F-13288 Marseille, France
  • Karl PetersenDepartment of Mathematics
    CB 3250 Phillips Hall
    University of North Carolina
    Chapel Hill, NC 27599, U.S.A.

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