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Entropy on abelian groupsDikranjan, Dikran N., 1950- ; Giordano Bruno, AnnaWe introduce the algebraic entropy for endomorphisms of arbitrary abelian groups, appropriately modifying existing notions of entropy. The basic properties of the algebraic entropy are given, as well ... as various examples. The main result of this paper is the Addition Theorem showing that the algebraic entropy is additive in appropriate sense with respect to invariant subgroups. We give several applications of the Addition Theorem, among them the Uniqueness Theorem for the algebraic entropy in the category of all abelian groups and their endomorphisms. Furthermore, we point out the delicate connection of the algebraic entropy with the Mahler measure and Lehmer Problem in Number Theory.Source: Advances in mathematics. - ISSN 0001-8708 (Vol. 298, 2016, str. 612-653)Type of material - article, component part ; adult, seriousPublish date - 2016Language - englishCOBISS.SI-ID - 17725017
Author
Dikranjan, Dikran N., 1950- |
Giordano Bruno, Anna
Topics
matematika |
diskretni dinamični sistemi |
algebraična entropija |
endomorfizem grupe |
Abelove grupe |
adicijski izrek |
Mahlerjeva mera |
Lehmerjev problem |
mathematics |
discrete dynamical system |
algebraic entropy |
group endomorphism |
Abelian group |
Addition Theorem |
Mahler measure |
Lehmer problem
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Dikranjan, Dikran N., 1950- | 28252 |
Giordano Bruno, Anna |
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