Topological conjugacy of constant length substitution dynamical systems

Ethan M. Coven, Michel Dekking, Mike Keane

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)91-107
Number of pages17
JournalIndagationes Mathematicae
Issue number1
Publication statusPublished - 2017


  • Conjugacy
  • Sliding block code
  • Substitution dynamical system
  • Thue–Morse substitution
  • Toeplitz substitution

Fingerprint Dive into the research topics of 'Topological conjugacy of constant length substitution dynamical systems'. Together they form a unique fingerprint.

Cite this