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C. Müllner, R. Yassawi:
"Automorphisms of automatic shifts";
Ergodic Theory and Dynamical Systems, First View (2020), 30 pages.

In this paper 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 non-trivial automorphisms arise from twisted compressions of another constant-length substitution. We characterize 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.

http://dx.doi.org/10.1017/etds.2020.13