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" Rigidity in higher rank Abelian group actions / "
Anatole Katok, Viorel NițicaG︣
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BL
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| Record Number
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631389
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dltt
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| Main Entry
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Katok, A. B
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| Title & Author
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Rigidity in higher rank Abelian group actions /\ Anatole Katok, Viorel NițicaG︣
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| Series Statement
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Cambridge tracts in mathematics ;; 185
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| Page. NO
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volume :: ill,; 24 cm
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| ISBN
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9780521879095
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: 0521879094
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| Notes
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volume 1. Introduction and cocycle problem
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| Contents
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Introduction: an overview -- Part I. Preliminaries from Dynamics and Analysis: -- 1. Definitions and properties of abelian group actions -- 2. Principal classes of algebraic actions -- 3. Preparatory results from analysis Part II. Cocycles, Cohomology and Rigidity: -- 4. First cohomology and rigidity for vector-valued cocycles -- 5. First cohomology and rigidity for general cocycles -- 6. Higher order cohomology. -- References. -- Index
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| Abstract
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"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems"--Back Cover
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"In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--P. 1
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"This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systemsIn a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"-- P.4 of back cover
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| Subject
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Rigidity (Geometry)
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| Subject
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Abelian groups
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| Dewey Classification
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512/.25
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| LC Classification
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QA640.77.K38 2011
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| Added Entry
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Nițica, Viorel
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