Automorphisms of [formula omitted]d-subshifts of finite type

Abstract

Let (Σ, σ) be a Z d -subshift of finite type. Under a strong irreducibility condition (strong specification), we show that Aut( Σ) contains any finite group. For Z d -subshift of finite type without strong specification, examples show that topological mixing is not sufficient to give any finite group in the automorphism group in general: in particular, End (Σ) may be an abelian semigroup. For an example of a topologically mixing Z 2 -subshift of finite type, the endomorphism semigroup and automorphism group are computed explicitly. This subshift has periodic-point permutations that do not extend to automorphisms.