Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem
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.
Cambridge University Press
Katok, Anatole and Nitica, Viorel, "Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem" (2011). College of Arts & Sciences Faculty Books. 92.