Using density matrices in classical dynamical systems
Mark Fannes (1998)
Banach Center Publications
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Displaying similar documents to “An axiomatic definition of the entropy of a -action on a Lebesgue space”
Using density matrices in classical dynamical systems
On regular generator of Z²-actions in exhaustive partitions
B. Kamiński (1987)
Studia Mathematica
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Slow entropy type invariants and smooth realization of commuting measure-preserving transformations
Anatole Katok, Jean-Paul Thouvenot (1997)
Annales de l'I.H.P. Probabilités et statistiques
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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 -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...
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.
On Two Conditional Entropies without Probability.
D. Vivona, M. Divari (2007)
Mathware and Soft Computing
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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 -actions on a Lebesgue space, we examine its basic properties and consider its behaviour in the class of product actions and rigid actions.
On extremal and perfect σ-algebras for -actions on a Lebesgue space
B. Kamiński, Z. Kowalski, P. Liardet (1997)
Studia Mathematica
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We show that for every positive integer d there exists a -action and an extremal σ-algebra of it which is not perfect.