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Eduardo Jorquera (2009)
Fundamenta Mathematicae
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We show that for a finitely generated group of C² circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.
Kyewon Koh Park, Uijung Lee (2004)
Studia Mathematica
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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.
Anatole Katok, Jean-Paul Thouvenot (1997)
Annales de l'I.H.P. Probabilités et statistiques
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Qing Zhang, Thomas Ward (1992)
Monatshefte für Mathematik
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Valentin Golodets, Sergey Sinel'shchikov (2000)
Colloquium Mathematicae
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The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
Richard Miles (2008)
Fundamenta Mathematicae
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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....
Brunon Kamiński, José de Sam Lazaro (2000)
Colloquium Mathematicae
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We investigate the properties of the entropy and conditional entropy of measurable partitions of unity in the space of essentially bounded functions defined on a Lebesgue probability space.
D. Vivona, M. Divari (2007)
Mathware and Soft Computing
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Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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François Blanchard (1993)
Bulletin de la Société Mathématique de France
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Thomas Hudetz (1998)
Banach Center Publications
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We define a new quantum dynamical entropy for a C*-algebra automorphism with an invariant state (and for an appropriate 'approximating' subalgebra), which entropy is a 'hybrid' of the two alternative definitions by Connes, Narnhofer and Thirring resp. by Alicki and Fannes (and earlier, Lindblad). We report on this entropy's properties and on three examples.