Displaying similar documents to “Spectral and mixing properties of actions of amenable groups.”

Spectrum of multidimensional dynamical systems with positive entropy

B. Kamiński, P. Liardet (1994)

Studia Mathematica

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Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov ℤ d -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to ℤ ∞ -actions. Next, using its relative version, we extend to ℤ ∞ -actions some other general results connecting spectrum and entropy.

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.

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.

The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups

Tim Austin (2016)

Analysis and Geometry in Metric Spaces

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Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof...

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.

Abelian groups of zero adjoint entropy

L. Salce, P. Zanardo (2010)

Colloquium Mathematicae

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The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of...

Relative spectral theory and measure-theoretic entropy of gaussian extensions

J.-P. Thouvenot (2009)

Fundamenta Mathematicae

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We describe the natural framework in which the relative spectral theory is developed. We give some results and indicate how they relate to two open problems in ergodic theory. We also compute the relative entropy of gaussian extensions of ergodic transformations.

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.