Algebraic entropy of generalized shifts on direct products

Abstract

For a set $Γ$, a function $λ:Γ\to Γ$ and a non-trivial abelian group $K$, the generalized shift $σ_λ:K^Γ\to K^Γ$ is defined by $(x_i)_{i\in Γ}\mapsto (x_{λ(i)})_{i\inΓ}$. In this paper we compute the algebraic entropy of $σ_λ$; it is either zero or infinite, depending exclusively on the properties of $λ$.