On the Density of Periodic Configurations in Strongly Irreducible Subshifts

Let G be a residually finite group and let A be a finite set. We prove that if X ⊂ A 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 ⊂ AZ, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense.