Entropy for endomorphisms of LCA groups
type: Item
instance of: scholarly article
title: Entropy for endomorphisms of LCA groups
zbMATH Open document ID: 1243.22007
author: Simone Virili
published in: Topology and its Applications
publication date: 2012-06-19T00:00:00Z
review text: The author introduces a modified version of the entropy defined for locally compact abelian groups by \textit{J. Peters} [Pac. J. Math. 96, 475--488 (1981; Zbl 0478.28010)]. The advantage of this approach is that it allows one to work with endomorphisms instead of automorphisms. After studying some of the basic properties of this new entropy the author gives and proves some formulae to compute the entropy of endomorphisms of \(\mathbb{Z}^N\), \(\mathbb{R}^N\) and \(\mathbb{C}^N\), for every positive integer \(N\).
reviewed by: Antonios Manoussos
Mathematics Subject Classification ID: 22D40
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 54C70
zbMATH DE Number: 6047981
zbMATH Keywords: algebraic entropy
zbMATH Keywords: locally compact abelian groups
zbMATH Keywords: Haar measure
zbMATH Keywords: continuous endomorphisms
MaRDI profile type: Publication
full work available at URL: j.topol.2011.02.017
OpenAlex ID: W2091561875
cites work: Topological Entropy
cites work: Entropy on abelian groups
cites work: Algebraic entropy for Abelian groups
cites work: New and old facts about entropy in uniform spaces and topological groups
cites work: Asymptotic Behavior of Products C p = C + ⋯+ C in Locally Compact Abelian Groups
cites work: Algebraic Yuzvinski formula
cites work: Q5723435
cites work: Automorphisms of solenoids and p-adic entropy
cites work: Entropy on discrete Abelian groups
cites work: Entropy of automorphisms on l.c.a. groups
cites work: Algebraic and other entropies of group endomorphisms
DOI: 10.1016/J.TOPOL.2011.02.017
description: scientific article; zbMATH DE number 6047981