Algebraic entropy of generalized shifts on direct products

Abstract

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

16 pages