Automorphisms of automatic shifts

Automorphisms of automatic shifts

In this article we continue the study of automorphism groups of constant length substitution shifts and also their topological factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other nontrivial automorphisms arise from {\em twisted} compressions...

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Veröffentlicht in:arXiv.org 2019-06
Hauptverfasser: Müllner, Clemens, Yassawi, Reem
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Automorphisms
Mathematics - Dynamical Systems
Roots
Substitutes
Topology
Work in process
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description In this article we continue the study of automorphism groups of constant length substitution shifts and also their topological factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other nontrivial automorphisms arise from {\em twisted} compressions of another constant length substitution. We characterise the group of roots of the identity in both the measurable and topological setting. Finally, we show that any topological factor of a constant length substitution shift is topologically conjugate to a constant length substitution shift via a letter-to-letter code.
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subjects Automorphisms
Mathematics - Dynamical Systems
Roots
Substitutes
Topology
Work in process
title Automorphisms of automatic shifts
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