Change search
ReferencesLink to record
Permanent link

Direct link
The entropy of algebraic actions of countable torsion-free abelian groups
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Fundamenta Mathematicae, ISSN 0016-2736, E-ISSN 1730-6329, Vol. 201, no 3, 261-282 p.Article in journal (Refereed) Published
Abstract [en]

This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured. The entropy of subactions is examined and, using a theorem of P. Samuel, it is shown that a mixing action of an infinitely generated group of finite rational rank cannot have a finitely generated subaction with finite non-zero entropy. Applications to the concept of entropy rank are also considered.

Place, publisher, year, edition, pages
2008. Vol. 201, no 3, 261-282 p.
Keyword [en]
entropy, algebraic action, torsion-free abelian group, Mahler measure, subaction, entropy rank
National Category
URN: urn:nbn:se:kth:diva-36335ISI: 000264414700004ScopusID: 2-s2.0-59549099883OAI: diva2:430623
Knut and Alice Wallenberg Foundation, KAW 2005.0098
QC 20110711Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2011-07-11Bibliographically approved

Open Access in DiVA

No full text


Search in DiVA

By author/editor
Miles, Richard
By organisation
Mathematics (Div.)
In the same journal
Fundamenta Mathematicae

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 27 hits
ReferencesLink to record
Permanent link

Direct link