Ergodic Theory and Dynamical Systems

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

a1 Faculté de Mathématiques et d'Informatique, Université de Picardie Jules Verne, 33, rue Saint Leu, 80039 Amiens Cedex, France (e-mail:


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.

(Received April 21 1998)
(Revised December 15 1998)