Entropy for endomorphisms of LCA groups

Simone Virili

doi:10.1016/j.topol.2011.02.017

Entropy for endomorphisms of LCA groups

Simone Virili

Research output: Contribution to journal › Article › Research › peer-review

17 Citations (Scopus)

Abstract

We introduce a modified version of the entropy defined for locally compact Abelian groups by Peters. This approach allows us to work with endomorphisms instead of working with automorphisms. We study some of the basic properties of this new entropy and we give direct proofs of the formulae that allow one to compute the entropy of endomorphisms of Z{double-struck} N, R{double-struck} N and C{double-struck} N, for every positive integer N. © 2012 Elsevier B.V.

Original language	English
Pages (from-to)	2546-2556
Journal	Topology and its Applications
Volume	159
Issue number	9
DOIs	https://doi.org/10.1016/j.topol.2011.02.017
Publication status	Published - 1 Jun 2012

Keywords

Algebraic entropy
Continuous endomorphisms
Haar measure
Locally compact abelian groups

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AB - We introduce a modified version of the entropy defined for locally compact Abelian groups by Peters. This approach allows us to work with endomorphisms instead of working with automorphisms. We study some of the basic properties of this new entropy and we give direct proofs of the formulae that allow one to compute the entropy of endomorphisms of Z{double-struck} N, R{double-struck} N and C{double-struck} N, for every positive integer N. © 2012 Elsevier B.V.

KW - Algebraic entropy

KW - Continuous endomorphisms

KW - Haar measure

KW - Locally compact abelian groups

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DO - 10.1016/j.topol.2011.02.017

M3 - Article

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EP - 2556

JO - Topology and its Applications

JF - Topology and its Applications

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