Topological conjugacy of constant length substitution dynamical systems

Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems. We show that each conjugacy class contains infinitely m...

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Bibliographic Details
Published in:Indagationes mathematicae 2017-02, Vol.28 (1), p.91-107
Main Authors: Coven, Ethan M., Michel Dekking, F., Keane, Michael S.
Format: Article
Language:English
Subjects:
Algorithms
Conjugacy
Dynamical systems
Sliding block code
Studies
Substitution dynamical system
Symbols
Thue–Morse substitution
Toeplitz substitution
Topology
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Summary:Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems. We show that each conjugacy class contains infinitely many substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue–Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they constitute a list of all primitive substitutions of length two with infinite minimal systems which are factors of the Thue–Morse system.
ISSN:0019-3577
1872-6100
DOI:10.1016/j.indag.2016.11.006