Slow entropy type invariants and smooth realization of commuting measure-preserving transformations

Anatole Katok; Jean-Paul Thouvenot

Displaying similar documents to “Slow entropy type invariants and smooth realization of commuting measure-preserving transformations”

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.

A note on the entropy of a doubly stochastic operator

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.

Entropy for noninvariant measures

Magda Komorníková, Jozef Komorník (1982)

Mathematica Slovaca

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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.

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.

Comparing measure theoretic entropy for $σ$ -finite measures with topological entropy

Magda Komorníková, Jozef Komorník (1983)

Mathematica Slovaca

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On Two Conditional Entropies without Probability.

D. Vivona, M. Divari (2007)

Mathware and Soft Computing

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On topological entropy

Riečan, B.

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Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

Annales de l’institut Fourier

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In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy $n$ -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity...