Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-36335ISI: 000264414700004Scopus ID: 2-s2.0-59549099883OAI: oai:DiVA.org:kth-36335DiVA: diva2:430623
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098
Note
QC 20110711Available from: 2011-07-11 Created: 2011-07-11 Last updated: 2017-12-11Bibliographically approved

Open Access in DiVA

No full text

Scopus

Search in DiVA

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

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 36 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf