Dynamical Entropy in Operator Algebras

• Κύριοι συγγραφείς: Neshveyev, Sergey (Συγγραφέας), Størmer, Erling (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Σειρά: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics ; 50
• Θέματα: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Operator theory.; Physics.; Operator Theory.; Functional Analysis.; Dynamical Systems and Ergodic Theory.; Theoretical, Mathematical and Computational Physics.

 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. 

 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.