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  • Entropy on abelian groups
    Dikranjan, Dikran N., 1950- ; Giordano Bruno, Anna
    We 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.
    Vir: Advances in mathematics. - ISSN 0001-8708 (Vol. 298, 2016, str. 612-653)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2016
    Jezik - angleški
    COBISS.SI-ID - 17725017

    Povezava(-e):

    http://dx.doi.org/10.1016/j.aim.2016.04.020

vir: Advances in mathematics. - ISSN 0001-8708 (Vol. 298, 2016, str. 612-653)

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