The stabilized automorphism group of odometers and of Toeplitz subshifts

TL;DR

This paper characterizes the stabilized automorphism groups of odometers and Toeplitz subshifts, demonstrating their invariance properties and showing that for torsion-free odometers, these groups serve as complete invariants.

Contribution

It provides a detailed characterization of stabilized automorphism groups and establishes their invariance, highlighting their role as isomorphism invariants for torsion-free odometers.

Findings

Stabilized automorphism groups are characterized for odometers and Toeplitz subshifts.

Invariance property of the stabilized automorphism group is proven.

For torsion-free odometers, the stabilized automorphism group is a full isomorphism invariant.

Abstract

We characterize the stabilized automorphism group for odometers and Toeplitz subshifts and then prove an invariance property of the stabilized automorphism group of these dynamical systems. A particular case of interest is that for torsion free odometers the stabilized automorphism group is a full isomorphism invariant.