کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425251 1633790 2016 42 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Entropy on abelian groups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Entropy on abelian groups
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 298, 6 August 2016, Pages 612-653
نویسندگان
, ,