For every finite-to-one map λ:Γ→Γ and for every abelian group K, the generalized shift σλ of the direct sum ⊕_Γ K is the endomorphism defined by (x_ i)↦(x_λ(i)). In this paper we analyze and compute the algebraic entropy of a generalized shift, which turns out to depend on the cardinality of K, but mainly on the function λ. We give many examples showing that the generalized shifts provide a very useful universal tool for producing counter-examples.

Algebraic entropy of shift endomorphisms on abelian groups

DIKRANJAN, Dikran;GIORDANO BRUNO, Anna;
2009

Abstract

For every finite-to-one map λ:Γ→Γ and for every abelian group K, the generalized shift σλ of the direct sum ⊕_Γ K is the endomorphism defined by (x_ i)↦(x_λ(i)). In this paper we analyze and compute the algebraic entropy of a generalized shift, which turns out to depend on the cardinality of K, but mainly on the function λ. We give many examples showing that the generalized shifts provide a very useful universal tool for producing counter-examples.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/877105
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