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Measure evolution of cellular automata and of finitely anticipative transformations

Published online by Cambridge University Press:  06 October 2015

PIERRE COLLET  and
SERVET MARTÍNEZ
PIERRE COLLET
Affiliation:
Centre de Physique Théorique, CNRS UMR 7644, Ecole Polytechnique F-91128 Palaiseau Cedex, France email [email protected]
SERVET MARTÍNEZ
Affiliation:
Departamento Ingeniería Matemática and Centro Modelamiento Matemático, Universidad de Chile, UMI 2807 CNRS, Casilla 170-3, Correo 3, Santiago, Chile email [email protected]
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Abstract

The evolution of cellular automata and of finitely anticipative transformations is studied by using right sets. These are the sets of symbols that are compatible with a past of a position and the respective coordinate of the transformation. Our main result shows, under some suitable conditions, that if the entropy converges to zero then the right sets increase towards the whole alphabet. We discuss these concepts with Wolfram automata.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 1 , February 2017 , pp. 129 - 145
Copyright
© Cambridge University Press, 2015 

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