For a set Γ, a function λ:Γ→Γ and a nontrivial abelian group K, the generalized shift σ_λ:K^Γ→K^Γ is defined by (x_i)↦(x_λ(i)). In this article we compute the algebraic entropy of σ_λ; it is either zero or infinite, depending exclusively on the properties of λ.
Algebraic entropy of shift endomorphisms on direct products
GIORDANO BRUNO, Anna
2010-01-01
Abstract
For a set Γ, a function λ:Γ→Γ and a nontrivial abelian group K, the generalized shift σ_λ:K^Γ→K^Γ is defined by (x_i)↦(x_λ(i)). In this article we compute the algebraic entropy of σ_λ; it is either zero or infinite, depending exclusively on the properties of λ.File in questo prodotto:
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IRIS-genshiftproduct.pdf
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