Introduction and cocycle problem
著者
書誌事項
Introduction and cocycle problem
（Cambridge tracts in mathematics, 185 . Rigidity in higher rank Abelian group actions ; v. 1）
Cambridge University Press, 2011
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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