9500869 de la Llave The project involves a broad based approach to problems of dynamics using methods from K.A.M. theory, hyperbolic dynamical systems and numerical exploration. In particular, we plan to study questions such as breakdown of invariant curves, rigidity of hyperbolic systems and variational methods. A study will be made of the long term behavior of systems whose evolution is known. The plan uses a broad based approach that combines analytical techniques and numerical explorations in such a way that they complement and reinforce each other. Many of the concrete problems that will be studied are motivated by hydrodynamics, for example, to compute the smallest amount of stirring that guarantees a thorough mixing. ***
