Algebraic Entropy of Generalized Shifts on Direct Products |
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Authors: | Anna Giordano Bruno |
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Institution: | 1. Dipartimento di Matematica Pura e Applicata , Università di Padova , Padova, Italy anna.giordanobruno@math.unipd.it |
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Abstract: | For a set Γ, a function λ: Γ → Γ and a nontrivial abelian group K, the \emphgeneralized shift σλ: K Γ → K Γ is defined by (x i ) i∈Γ ? (x λ(i)) i∈Γ 3
Ayatollah Zadeh Shirazi , F. ,
Heidari Ardi , F. ,
Karami Kabir , N. ( 2008 ). A note on shift theory . Math. Pannon. 19 : 187 – 195 . Google Scholar]]. In this article we compute the algebraic entropy of σλ; it is either zero or infinite, depending exclusively on the properties of λ. This solves two problems posed in 2
Akhavin , M. ,
Ayatollah Zadeh Shirazi , F. ,
Dikranjan , D. ,
Giordano Bruno , A. ,
Hosseini , A. ( 2009 ). Algebraic entropy of shift endomorphisms on abelian groups . Quaest. Math. 32 : 529 – 550 .Crossref], Web of Science ®] , Google Scholar]]. |
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Keywords: | Abelian group Algebraic entropy Generalized shift Shift |
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