On a substitution subshift related to the Grigorchuk group

TL;DR

This paper investigates a substitution subshift connected to the Grigorchuk group, demonstrating its conjugacy to the binary odometer except for a countable set, thus revealing its underlying dynamical structure.

Contribution

It establishes a conjugacy between a specific substitution subshift related to the Grigorchuk group and the binary odometer, clarifying its dynamical behavior.

Findings

Substitution subshift is conjugate to the binary odometer

The conjugacy holds up to a countable set

Provides insight into the dynamics of systems related to the Grigorchuk group

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.