On the conjugacy class of the Fibonacci dynamical system

Journal article (2017)

Authors

F.M. Dekking Applied Probability - EEMCS
M.S. Keane Applied Probability - EEMCS , New York University Shanghai
Research Group
Applied Probability (EEMCS) (TU Delft)
Fibonacci word Automatic sequences Topological conjugacy Symbolic dynamical system
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

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.