Local rigidity of partially hyperbolic actions I. KAM method and ℤ<sup><i>k</i></sup>actions on the torus
Local rigidity of partially hyperbolic actions I. KAM method and ℤ<sup><i>k</i></sup>actions on the torus
We show C 1 local rigidity for ޚ k .k2/ 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 ޔ N for any even N 6.