Mathematical Sciences: Hamiltonian Dynamics

小行星9627979 本计画利用变分技巧来证明保守动力系统中许多不同拓扑类型的轨道的存在性。此外，研究者将考虑由J.Lasker引入的频率分析方法，并将其应用于检测保守系统中的混沌和扩散。提出的目标之一是给拉斯克的方法，目前主要是一个数值方法的坚实的数学基础。 动力系统中的混沌和扩散现象在物理世界中有着广泛的应用。例如，它们可以用来模拟某些涉及湍流和突然分叉的天气系统。

9627979 Gole This project uses variational techniques to prove the existence of orbits of many different topological types in conservative dynamical systems. In addition, the investigator will consider the method of frequency analysis introduced by J. Lasker and apply them to detect chaos and diffusion in conservative systems. One of the proposed goals is to give a firm mathematical foundation of Lasker's method, which at present is mostly a numerical method. Chaos and diffusion phenomena in dynamical systems have wide ranging applications in the physical world. For example, they can be used to model certain weather systems involving turbulence and sudden bifurcation.