On the conjugacy class of the Fibonacci dynamical system

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We characterize the symbolical dynamical systems which are topologically isomorphic to the Fibonacci dynamical system. We prove that there are infinitely many injective primitive substitutions generating a dynamical system in the Fibonacci conjugacy class. In this class there are infinitely many dynamical systems not generated by a substitution. An example is the system generated by doubling the 0's in the infinite Fibonacci word.

Original languageEnglish
Pages (from-to)59-69
Number of pages11
JournalTheoretical Computer Science
Publication statusPublished - 2017


  • Automatic sequences
  • Fibonacci word
  • Symbolic dynamical system
  • Topological conjugacy


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