The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On the directional entropy for ℤ²-actions on a Lebesgue space”

On the entropy for group actions on the circle

Eduardo Jorquera (2009)

Fundamenta Mathematicae

Similarity:

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.

Entropy pairs of ℤ² and their directional properties

Kyewon Koh Park, Uijung Lee (2004)

Studia Mathematica

Similarity:

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.

Complete positivity of entropy and non-Bernoullicity for transformation groups

Valentin Golodets, Sergey Sinel'shchikov (2000)

Colloquium Mathematicae

Similarity:

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.

The entropy of algebraic actions of countable torsion-free abelian groups

Richard Miles (2008)

Fundamenta Mathematicae

Similarity:

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....

A note on the entropy of a doubly stochastic operator

Brunon Kamiński, José de Sam Lazaro (2000)

Colloquium Mathematicae

Similarity:

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.

Quantum dynamical entropy revisited

Thomas Hudetz (1998)

Banach Center Publications

Similarity:

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.