Exponential mixing, KAM and smooth local rigidity
Abstract
Consider actions of r by ergodic automorphisms on a compact nilmanifolds for r ≥ 2. We show that small Ck perturbations of such higher rank partially hyperbolic actions are smoothly conjugate to the original action, using a KAM scheme. The driving force for convergence of this iteration is the exponential mixing of the original action.
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