Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 319-334
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Ya. Vorobets. On a substitution subshift related to the Grigorchuk group. Informatics and Automation, Differential equations and topology. II, Tome 271 (2010), pp. 319-334. http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a20/
@article{TRSPY_2010_271_a20,
author = {Ya. Vorobets},
title = {On a~substitution subshift related to the {Grigorchuk} group},
journal = {Informatics and Automation},
pages = {319--334},
year = {2010},
volume = {271},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a20/}
}
TY - JOUR
AU - Ya. Vorobets
TI - On a substitution subshift related to the Grigorchuk group
JO - Informatics and Automation
PY - 2010
SP - 319
EP - 334
VL - 271
UR - http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a20/
LA - en
ID - TRSPY_2010_271_a20
ER -
%0 Journal Article
%A Ya. Vorobets
%T On a substitution subshift related to the Grigorchuk group
%J Informatics and Automation
%D 2010
%P 319-334
%V 271
%U http://geodesic.mathdoc.fr/item/TRSPY_2010_271_a20/
%G en
%F TRSPY_2010_271_a20
We study the dynamics of a substitution subshift given by the substitution $a\to aca$, $b\to d$, $c\to b$, $d\to c$, which is related to the Grigorchuk group. This dynamical system is shown to be, up to a countable set, conjugate to the binary odometer.
[1] Bezuglyi S., Kwiatkowski J., Medynets K., “Aperiodic substitution systems and their Bratteli diagrams”, Ergodic Theory and Dyn. Syst., 29:1 (2009), 37–72 | DOI | MR | Zbl
[2] Downarowicz T., “Survey of odometers and Toeplitz flows”, Algebraic and topological dynamics, Contemp. Math., 385, Amer. Math. Soc., Providence (RI), 2005, 7–37 | DOI | MR | Zbl
[3] Grigorchuk R., “Solved and unsolved problems around one group”, Infinite groups: geometric, combinatorial and dynamical aspects, Progr. Math., 248, Birkhäuser, Basel, 2005, 117–218 | DOI | MR | Zbl
