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Linearly recurrent subshifts have a finite number of non-periodic subshift factors

Published online by Cambridge University Press:  01 August 2000

FABIEN DURAND
FABIEN DURAND
Affiliation:
Faculté de Mathématiques et d'Informatique, Université de Picardie Jules Verne, 33, rue Saint Leu, 80039 Amiens Cedex, France (e-mail: [email protected])
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Abstract

A minimal subshift $(X,T)$ is linearly recurrent (LR) if there exists a constant $K$ so that for each clopen set $U$ generated by a finite word, $u$, the return time to $U$, with respect to $T$, is bounded by $K|u|$. We prove that given a LR subshift $(X,T)$ the set of its non-periodic subshift factors is finite up to isomorphism. We also give a constructive characterization of these subshifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 4 , August 2000 , pp. 1061 - 1078
Copyright
2000 Cambridge University Press

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