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Linearly recurrent subshifts have a finite number of non-periodic subshift factors. (English) Zbl 0965.37013
Ergodic Theory Dyn. Syst. 20, No. 4, 1061-1078 (2000); corrigendum and addendum 23, No. 2, 663-669 (2003).
This paper may be considered as an extension of F. Durand B. Host and C. Skau [ibid. 19, 953-993 (1999; Zbl 1044.46543)]. The author proves that for each linearly recurrent subshift (two-sided) the set of its non-periodic subshift factors is finite up to isomorphism. By definition, a subshift is linearly recurrent if it is minimal and there exists a constant $$K$$ such that for any closed and open set $$U$$ generated by a word $$u$$ of length $$|u|$$, the return time to $$U$$ is bounded by $$K|u|$$.
Added in 2007: Summary: We prove that a subshift $$(X,T)$$ is linearly recurrent if and only if it is a primitive and proper $$S$$-adic subshift. This corrects Proposition 6 in the paper cited in the heading.

##### MSC:
 37B10 Symbolic dynamics 37B20 Notions of recurrence and recurrent behavior in topological dynamical systems 11B85 Automata sequences 54H20 Topological dynamics (MSC2010)
##### Keywords:
symbolic dynamics; shift; subshift; return time
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