On the density of periodic configurations in strongly irreducible subshifts

Details On the density of periodic configurations in strongly irreducible subshifts On the density of periodic configurations in strongly irreducible subshifts

2011-10-21

arxiv.org/abs/1110.4921v3

Mathematics

Dynamical Systems

Scientific paper

Let $G$ be a residually finite group and let $A$ be a finite set. We prove that if $X \subset A^G$ is a strongly irreducible subshift of finite type containing a periodic configuration then periodic configurations are dense in $X$. The density of periodic configurations implies in particular that every injective endomorphism of $X$ is surjective and that the group of automorphisms of $X$ is residually finite. We also introduce a class of subshifts $X \subset A^\Z$, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense.

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