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Dynamical Entropy in Operator Algebras [electronic resource] / by Sergey Neshveyev, Erling Stȹrmer.

Por: Neshveyev, Sergey [author.]Colaborador(es): Stȹrmer, Erling [author.]Tipo de material: TextoTextoSeries Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 50Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006Descripción: IX, 296 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783540346739Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Differentiable dynamical systems | Functional analysis | Operator theory | Mathematical physics | Mathematics | Operator Theory | Functional Analysis | Dynamical Systems and Ergodic Theory | Mathematical and Computational PhysicsFormatos físicos adicionales: Sin títuloClasificación CDD: 515.724 Clasificación LoC:QA329-329.9Recursos en línea: de clik aquí para ver el libro electrónico
Contenidos:
Springer eBooksResumen: During the last 30 years there have been several attempts at extending the notion of entropy to noncommutative dynamical systems. The authors present in the book the two most successful approaches to the extensions of measure entropy and topological entropy to the noncommutative setting and analyze in detail the main models in the theory. The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.
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General Theory -- Classical Dynamical Systems -- Relative Entropy -- Dynamical Entropy -- Maximality of Entropy and Commutativity -- Dynamical Abelian Models -- Topological Entropy -- Dynamics on the State Space -- Crossed Products -- Variational Principle -- Special Topics -- Relative Entropy and Subfactors -- Systems of Algebraic Origin -- Binary Shifts -- Bogoliubov Automorphisms -- Free Products.

During the last 30 years there have been several attempts at extending the notion of entropy to noncommutative dynamical systems. The authors present in the book the two most successful approaches to the extensions of measure entropy and topological entropy to the noncommutative setting and analyze in detail the main models in the theory. The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

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