Geodesic
Constructive symbolic presentations of rank one measure-preserving systems
Terrence Adams1 ; Sébastien Ferenczi2 ; Karl Petersen3
1 U.S. Government 9800 Savage Rd Ft. Meade, MD 20755, U.S.A.
2 Aix Marseille Université CNRS, Centrale Marseille Institut de Mathématiques de Marseille I2M–UMR 7373 F-13288 Marseille, France
3 Department of Mathematics CB 3250 Phillips Hall University of North Carolina Chapel Hill, NC 27599, U.S.A.
Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 243-255.

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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.
DOI : 10.4064/cm7124-3-2017
Keywords: given rank measure preserving system defined cutting stacking spacers produce rank binary sequence its orbit closure under shift transformation its unique nonatomic invariant probability isomorphic given system particular classical dyadic odometer presented terms recursive sequence blocks two symbol alphabet construction accomplished using definition rank setting adic bratteli vershik systems

Terrence Adams 1 ; Sébastien Ferenczi 2 ; Karl Petersen 3

1 U.S. Government 9800 Savage Rd Ft. Meade, MD 20755, U.S.A.
2 Aix Marseille Université CNRS, Centrale Marseille Institut de Mathématiques de Marseille I2M–UMR 7373 F-13288 Marseille, France
3 Department of Mathematics CB 3250 Phillips Hall University of North Carolina Chapel Hill, NC 27599, U.S.A. 
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Terrence Adams; Sébastien Ferenczi; Karl Petersen. Constructive symbolic presentations of rank one measure-preserving systems. Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 243-255. doi : 10.4064/cm7124-3-2017. http://geodesic.mathdoc.fr/articles/10.4064/cm7124-3-2017/

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