Preservation of an invariant torus under perturbation

There is presented a new approach to the theory of perturbation of invariant toroidal manifolds of dynamical systems related to use of Green's functions for a linearized problem. This approach permits the presentation, from a single and general point of view, of the theory of perturbation of smooth as well as of nondifferentiable invariant manifolds of dynamical systems, and also permits the proof of new theorems on the existence of such manifolds.