Mathematical Sciences: Analytic and Numerical Methods for the Study of Long Term Behavior

9500869 de la Llave这个项目涉及一个广泛的方法来解决动力学问题，使用K.A.M.理论、双曲动力系统和数值探索的方法。特别是，我们计划研究诸如不变曲线的分解、双曲系统的刚性和变分方法等问题。将对已知演化的系统的长期行为进行研究。该计划采用了广泛的方法，结合了分析技术和数值探索，使它们相互补充和加强。许多将要研究的具体问题都是由流体动力学引起的，例如，计算保证充分混合的最小搅拌量。＊＊＊

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. ***