KAM Theory without action--angle variables
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Given a torus approximately invariant under a symplectic map, we find sufficient conditions for the existence of a true invariant torus close to the given one. We do not assume either that we are working on action-angle variables nor that the map is close to integrable. The proposed method is also useful to compute numerically invariant tori for symplectic maps. Analogous results are also true for vector fields.