Automorphisms of automatic shifts

Clemens Müllner (1) , Reem Yassawi (2)

1 Institut für Diskrete Mathematik und Geometrie [Wien]
2 CTN - Combinatoire, théorie des nombres

In this article we continue the study of automorphism groups of constant length substitution shifts and also their topolog-ical factors. We show that up to conjugacy, all roots of the identity map are letter exchanging maps, and all other nontrivial automor-phisms arise from twisted compressions of another constant length substitution. We characterise the group of roots of the identity. Finally, we show that any topological factor of a constant length substitution shift is topologically conjugate to a constant length substitution shift.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Clemens Müllner, Reem Yassawi. Automorphisms of automatic shifts. Ergodic Theory and Dynamical Systems, 2021, 41 (5), pp.1530-1559. ⟨10.1017/etds.2020.13⟩. ⟨hal-02093714⟩