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Coding of substitution dynamical systems as shifts of finite type

Published online by Cambridge University Press:  06 November 2014

PAUL SURER
PAUL SURER*
Affiliation:
Departamento de Matemática, IBILCE - UNESP, São José do Rio Preto, Brazil email me@palovsky.com
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Abstract

We develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shifts of finite type in many different ways. The well-known prefix–suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights into the theory of substitution dynamical systems and might serve as a powerful tool for further researches.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 944 - 972
Copyright
© Cambridge University Press, 2014 

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