Local rigidity of partially hyperbolic actions I. KAM method and Zk actions on the torus

被引：38

作者：

Damjanovic, Danijela ^{[1
]}

Katok, Anatole ^{[2
]}

机构：

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

[2] Penn State Univ, Dept Math, State Coll, PA 16802 USA

来源：

ANNALS OF MATHEMATICS | 2010年 / 172卷 / 03期

基金：

美国国家科学基金会;

关键词：

RANK ABELIAN-GROUPS; TORAL AUTOMORPHISMS; LATTICE ACTIONS; LIE-GROUPS; COHOMOLOGY;

D O I：

10.4007/annals.2010.172.1805

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show C-infinity local rigidity for Z(k) (k >= 2) higher rank partially hyperbolic actions by toral automorphisms, using a generalization of the KAM (Kolmogorov-Arnold- Moser) iterative scheme. We also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus T-N for any even N >= 6.

引用

页码：1805 / 1858

页数：54

共 38 条

[1]

[Anonymous], 1977, LECT NOTES MATH

[2] Rigidity of isometric lattice actions on compact Riemannian manifolds [J].