Constructive symbolic presentations of rank one measure-preserving systems
Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 243-255
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Terrence Adams 1 ; Sébastien Ferenczi 2 ; Karl Petersen 3
@article{10_4064_cm7124_3_2017,
author = {Terrence Adams and S\'ebastien Ferenczi and Karl Petersen},
title = {Constructive symbolic presentations of rank one measure-preserving systems},
journal = {Colloquium Mathematicum},
pages = {243--255},
year = {2017},
volume = {150},
number = {2},
doi = {10.4064/cm7124-3-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm7124-3-2017/}
}
TY - JOUR AU - Terrence Adams AU - Sébastien Ferenczi AU - Karl Petersen TI - Constructive symbolic presentations of rank one measure-preserving systems JO - Colloquium Mathematicum PY - 2017 SP - 243 EP - 255 VL - 150 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm7124-3-2017/ DO - 10.4064/cm7124-3-2017 LA - en ID - 10_4064_cm7124_3_2017 ER -
%0 Journal Article %A Terrence Adams %A Sébastien Ferenczi %A Karl Petersen %T Constructive symbolic presentations of rank one measure-preserving systems %J Colloquium Mathematicum %D 2017 %P 243-255 %V 150 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/cm7124-3-2017/ %R 10.4064/cm7124-3-2017 %G en %F 10_4064_cm7124_3_2017
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
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