Accurate Strategies for K.A.M. Bounds and Their Implementation

We study perturbative expansions for quasi-periodic solutions of non—linear systems. We describe how to construct and implement algorithms that prove convergence of these expansions for values of the perturbation parameter as close to optimal as desired. The method is based on a constructive form of K.A.M. theory and implemented using interval arithmetic. For some cases, the algorithms have been run on a computer yielding results better than 90% of optimal.

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