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

9500869 德拉亚韦 该项目涉及一个基础广泛的方法来解决问题的动力学 使用K.A.M.理论，双曲动力系统和 数值探索特别是，我们计划研究以下问题， 不变曲线的分解，双曲系统的刚性， 变分法 将研究系统的长期行为， 进化是已知的。 该计划采用基础广泛的方法， 结合分析技术和数值探索，在这样一个 它们是相互补充和加强的。 许多 将研究的具体问题是由流体力学激发的，例如，计算最小搅拌量， 确保彻底混合。 ***

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. ***