This project is mathematical research in perturbation theory for problems in classical mechanics and related areas. The essential difficulty to be overcome is that one is working near resonances that lead to very large terms in the perturbation expansion. These are overcome by the techniques of the so-called K.A.M. theory, which gives a more sophisticated way of handling such perturbations. The numerical bounds given by a straightforward application of K.A.M. are not sharp. The main objective of the present project is to sharpen the bounds to values that are close to best possible. The method is to explore various strategies for obtaining the bounds by use of a computer program that automates the process of finding rigorous bounds through the use of a sort of interval arithmetic in Banach spaces of functions.
