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EnglishWe 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.
| Titolo: | Entropy on abelian groups |
| Autori: | GIORDANO BRUNO, Anna (Corresponding) |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Abstract: | 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. |
| Handle: | http://hdl.handle.net/11390/1091764 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| halg.pdf | Articolo principale, Accesso Aperto MIUR | Versione Editoriale (PDF) |  | Open Access Visualizza/Apri |
| schedaprogetto.pdf | Scheda di progetto | Altro materiale allegato |  | Open Access Visualizza/Apri |
http://hdl.handle.net/11390/1091764
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