Rigidity in Higher Rank Abelian Group Actions
Volume 1. Introduction and Cocycle Problem
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Part of Cambridge Tracts in Mathematics
- Anatole Katok, Pennsylvania State University
- Viorel Niţică, West Chester University, Pennsylvania
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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.Read more
- Builds a bridge between classical and emerging theory and emphasizes the new phenomena that appear
- Includes a chapter providing preparatory results in analysis
- Contains a large collection of examples of higher rank Anosov and partially hyperbolic actions
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"This very welcome addition to the literature is the first book-length introduction to the rigidity of higher rand abelian group actions."
David Michael Fisher for Mathematical Reviews
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- Date Published: June 2011
- format: Adobe eBook Reader
- isbn: 9781139088978
- contains: 3 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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
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