Geodesic
On a~substitution subshift related to the Grigorchuk group
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 319-334

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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. 
@article{TM_2010_271_a20,
     author = {Ya. Vorobets},
     title = {On a~substitution subshift related to the {Grigorchuk} group},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {319--334},
     publisher = {mathdoc},
     volume = {271},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_271_a20/}
}
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Ya. Vorobets. On a~substitution subshift related to the Grigorchuk group. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 319-334. http://geodesic.mathdoc.fr/item/TM_2010_271_a20/