Algebraic entropy of generalized shifts on direct products

Details Algebraic entropy of generalized shifts on direct products Algebraic entropy of generalized shifts on direct products

2010-06-27

arxiv.org/abs/1006.5208v1

Comm. Algebra 38 (11) (2010), 4155-4174

Mathematics

Group Theory

16 pages

Scientific paper

10.1080/00927870903337984

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 $\lambda$.

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