Mathematical Sciences: Computational Research on Dynamical Systems

该项目支持动力系统的研究，重点是计算。提案中讨论的具体项目有：1。希尔伯特第十六题：平面上多项式向量场极限环数的数值和符号计算。2. 由流体边界层方程导出的矢量场动力学研究。3. 用MACSYMA实现常微分方程问题的摄动方法。4. 多元分岔点附近微分方程多参数系统的研究。5. 复Henon映射的数值研究，复二空间的全纯微分同构。6. 三维流动周期轨道多项式结不变量的符号计算。更广泛地说，该项目将支持动态系统研究的算法和高效计算环境的发展。

This project supports resear5ch in dynamical systems with significant emphasis on computation. The specific projects discussed in the proposal are: 1. Hilbert's 16th Problem: Numerical and symbolic computations to obtain bounds on the number of limit cycles possessed by polynomial vector fields in the plane. 2. Dynamical studies of vector fields derived from equations of fluid boundary layers. 3. The implementation of perturbation methods for ordinary differential equations problems using MACSYMA. 4. The study of multiparameter systems of differential equations near points of multiple bifurcation. 5. Numerical studies of the complex Henon mapping, holomorphic diffeomorphism of complex two space. 6. Symbolic computation of polynomial knot invariants associated to periodic orbits of three dimensional flows. More broadly, the project will support the development of algorithms and efficient computing environments for the studies of dynamical systems.