# Local rigidity of partially hyperbolic actions I. KAM method and \${\mathbb Z^k}\$ actions on the torus | Annals of Mathematics

Abstract We show ℂ∞ local rigidity for ℤk (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

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### 数学年刊（Annals of Mathematics）

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