On the density of periodic configurations in strongly irreducible subshifts

Abstract

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 $X\subset A^{\mathbb{Z}}$, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense.

References in corpus (1)

• Periodic configurations of subshifts on groups

Cited by in corpus (2)

• Cellular automata between sofic tree shifts
• Verification of mixing properties in two-dimensional shifts of finite type