On the conjugacy class of the Fibonacci dynamical system

F. Michel Dekking; Michael S. Keane

doi:10.1016/j.tcs.2017.01.009

On the conjugacy class of the Fibonacci dynamical system

F. Michel Dekking^*, Michael S. Keane

^*Corresponding author for this work

Applied Probability

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	59-69
Number of pages	11
Journal	Theoretical Computer Science
Volume	668
DOIs	https://doi.org/10.1016/j.tcs.2017.01.009
Publication status	Published - 2017

Keywords

Automatic sequences
Fibonacci word
Symbolic dynamical system
Topological conjugacy

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10.1016/j.tcs.2017.01.009

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title = "On the conjugacy class of the Fibonacci dynamical system",

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.",

keywords = "Automatic sequences, Fibonacci word, Symbolic dynamical system, Topological conjugacy",

author = "Dekking, {F. Michel} and Keane, {Michael S.}",

year = "2017",

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AU - Dekking, F. Michel

AU - Keane, Michael S.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Automatic sequences

KW - Fibonacci word

KW - Symbolic dynamical system

KW - Topological conjugacy

UR - http://www.scopus.com/inward/record.url?scp=85009809229&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2017.01.009

DO - 10.1016/j.tcs.2017.01.009

M3 - Article

AN - SCOPUS:85009809229

SN - 0304-3975

VL - 668

SP - 59

EP - 69

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -

On the conjugacy class of the Fibonacci dynamical system

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Keywords

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