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

• 成果类型: Article
• 署名作者: Damjanovic, Danijela; Katok, Anatole
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.1805
• 发表日期: 2010
• 页码: 1805-1858
• 关键词: rank abelian-groups; toral automorphisms; lattice actions; lie-groups; COHOMOLOGY

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.