| 1 LOCAL RIGIDITY OF PARTIALLY HYPERBOLIC ACTIONS I. KAM METHOD AND Z k ACTIONS ON THE TORUS (2009) | |||||||||||||||
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| ABSTRACT. We show C ∞ local rigidity for Z k (k ≥ 2) higherrank 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. 1. | |||||||||||||||
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