Displaying similar documents to “The Abramov-Rokhlin Entropy Addition Formula for Amenable Group Actions.”

On the directional entropy for ℤ²-actions on a Lebesgue space

B. Kamiński, K. Park (1999)

Studia Mathematica

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We define the concept of directional entropy for arbitrary ℤ 2 -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.

On the entropy for group actions on the circle

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.

Entropy pairs of ℤ² and their directional properties

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.

When every point is either transitive or periodic

Tomasz Downarowicz, Xiangdong Ye (2002)

Colloquium Mathematicae

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We study transitive non-minimal ℕ-actions and ℤ-actions. We show that there are such actions whose non-transitive points are periodic and whose topological entropy is positive. It turns out that such actions can be obtained by perturbing minimal systems under some reasonable assumptions.

Complete positivity of entropy and non-Bernoullicity for transformation groups

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.