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

摘要

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.