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Automorphisms of automatic shifts

Part of: Sequences and sets Topological dynamics

Published online by Cambridge University Press:  20 February 2020

CLEMENS MÜLLNER Open the ORCID record for CLEMENS MÜLLNER [Opens in a new window]  and
REEM YASSAWI
CLEMENS MÜLLNER
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, 69100 Villeurbanne, France Discrete Mathematics and Geometry, TU Wien, Wiedner Hauptstr. 8, 1040 Wien, Austria
REEM YASSAWI
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 novembre 1918, 69100 Villeurbanne, France School of Mathematics and Statistics, Walton Hall, Kents Hill, Milton Keynes, MK76AA, UK
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Abstract

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.

Keywords

substitution dynamical systemsautomatic sequencesautomorphisms

MSC classification

Primary: 37B10: Symbolic dynamics 11B85: Automata sequences
Secondary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37B15: Cellular automata
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 5 , May 2021 , pp. 1530 - 1559
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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