Rigidity in higher rank Abelian group actions
By: Anatole Katok, Viorel Nițica︣
Contributors: Nițica, Viorel
Series: Cambridge tracts in mathematics -- 185-; Cambridge tracts in mathematics -- 185-
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge, UK; New York
Language: eng
ISBN-13: 9780521879095
Subjects: Rigidity (Geometry); Abelian groups
Description: "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"--

"In a very general sense modern theory of smooth dynamical systems deals with smooth actions of "sufficiently large but not too large" groups or semigroups (usually locally compact but not compact) on a "sufficiently small" phase space (usually compact, or, sometimes, finite volume manifolds). Important branches of dynamics specifically consider actions preserving a geometric structure with an infinite-dimensional group of automorphisms, two principal examples being a volume and a symplectic structure. The natural equivalence relation for actions is differentiable (corr. volume preserving or symplectic) conjugacy"--
Notes: v. 1. Introduction and cocycle problem