v. 1. Introduction and cocycle problem
|Statement||Anatole Katok, Viorel Nițica︣|
|Series||Cambridge tracts in mathematics -- 185-, Cambridge tracts in mathematics -- 185-|
|LC Classifications||QA640.77 .K38 2011|
|The Physical Object|
|Pagination||1 v. ;|
|LC Control Number||2011006030|
Get this from a library! Rigidity in higher rank Abelian group actions. [A B Katok; Viorel Nițica] -- "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. Rigidity in Higher Rank Abelian Group Actions: Volume 1, Introduction and Cocycle Problem Anatole Katok, Viorel Nitica This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. Get this from a library! Rigidity in higher rank Abelian group actions. Vol. I, Introduction and cocycle problem. [A B Katok; Viorel Nițica] -- "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 the other hand, higher rank abelian Anosov actions enjoy more rigidity in this aspect. An action is said to be C 1-locally rigid if all C-perturbations are C1-conjugate to the original action. Local rigidity was rst proved for Cartan actions on tori by Katok and Lewis [KL91], and later extended to some quite general classes of actions in the.
Di erential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions A. Katok and R. J. Spatzier y To Dmitry Viktorovich Anosov on his sixtieth birthday Abstract We show that most homogeneous Anosov actions of higher rank Abelian groups are locally C1-rigid (up to an automorphism). This result is the main part in the. We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber. rank semi-simple Lie groups, where here higher rank means that all simple factors have real rank at least 2. (See subsection for a deﬁnition of rank.) Fairly early in the theory it became clear that local rigidity often held, and was in fact easier to prove, for certain actions of higher rank abelian groups, i.e. Zk for k≥2, see [KL1]. S. Hurder [28, 29] proved inﬁnitesimal and deformation rigidity, respectively, of these actions, Hurder by analyzing higher rank abelian subgroups and their dynamical properties. These results were just shy of local rigidity. Let us ﬁrst coin the relevant notions. We let ¡ be a ﬁnitely generated group, and ‰: ¡! Diff1M an action of ¡.
Rigidity for actions of higher rank abelian groups The goal of this monograph and its projected sequel is to give an up-to-date and, as much as possible, self-contained presentation of certain. Katok A, Spatzier R () Differential rigidity of Anosov actions of higher rank abelian groups and algebraic lattice actions. Trudy Mat Inst Stek – MathSciNet Google Scholar Character rigidity for lattices in higher-rank groups Jesse Peterson Octo Abstract We show that if is an irreducible lattice in a higher rank center-free semi-simple Lie group with no compact factors and having property (T) of Kazhdan, then is operator algebraic superrigid, i.e., any unitary representation of which generates a II. DIFFERENTIABLE RIGIDITY OF HIGHER RANK ABELIAN GROUP ACTIONS joint with Viorel Nitica (to appear in Cambridge University Press) as well as from some published articles will be provided as course notes. SYLLABUS 1. PRELIMINARIES (approx. one lecture) Differentiable, topological and measure-preserving group actions.