Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem by Anatole KatokRigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem by Anatole Katok

Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem

byAnatole Katok, Viorel Niţică

Hardcover | July 25, 2011

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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.
Title:Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle ProblemFormat:HardcoverDimensions:320 pages, 8.98 × 5.98 × 0.75 inPublished:July 25, 2011Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521879094

ISBN - 13:9780521879095

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Table of Contents

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.