Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem (Google eBook)

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Cambridge University Press, Jun 16, 2011 - Mathematics
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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.
  

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Contents

Introduction an overview
1
Part I Preliminaries from dynamics and analysis
9
Part II Cocycles cohomology and rigidity
131
References
302
Index
311
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About the author (2011)

Anatole Katok is Raymond N. Shibley Professor of Mathematics at Pennsylvania State University.

Viorel Nitica is Professor of Mathematics at West Chester University, Pennsylvania.

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