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Entropy range problems and actions of locally normal groups
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2009 (English)In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 25, no 3, 981-989 p.Article in journal (Refereed) Published
Abstract [en]

This paper deals with the problem of finding the range of entropy values resulting from actions of discrete amenable groups by automorphisms of compact abelian groups. When the acting group G is locally normal, we obtain an entropy formula and show that the full range of entropy values [0, infinity] occurs for actions of G. We consider related entropy range problems, give sufficient conditions for zero entropy and, as a consequence, verify the known relationship between completely positive entropy and mixing for these actions.

Place, publisher, year, edition, pages
2009. Vol. 25, no 3, 981-989 p.
Keyword [en]
Entropy, entropy range, algebraic action, locally normal group, Lehmer's problem
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-32376DOI: 10.3934/dcds.2009.25.981ISI: 000269221200014Scopus ID: 2-s2.0-72549111514OAI: oai:DiVA.org:kth-32376DiVA: diva2:410409
Funder
Knut and Alice Wallenberg Foundation, KAW 2005.0098
Note
QC 20110413Available from: 2011-04-13 Created: 2011-04-13 Last updated: 2017-12-11Bibliographically approved

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