On a substitution subshift related to the Grigorchuk group

2009/10/26 by Yaroslav Vorobets, Vorobets, Yaroslav
Computer Science · Mathematics · Materials Science · #semigroups and automata theory #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.0910.4800

Abstract

We study dynamics of a substitution subshift given by the substitution a->aca, b->d, c->b, d->c that is related to the Grigorchuk group. This dynamical system is shown to be, up to a countable set, conjugated to the binary odometer.

Related

• On the topological full group containing the Grigorchuk group
• Substitutional subshifts and growth of groups
• The stabilized automorphism group of odometers and of Toeplitz subshifts
• SFT covers for actions of the first Grigorchuk group
• Schreier graphs of Grigorchuk's group and a subshift associated to a non-primitive substitution