Mathematical Sciences: Symplectic Methods in Bifuration Theory, Hamiltonian Dynamics, and Lie Theory

9503273比率拟议的研究涉及动力系统和几何力学领域。具体地说，提出了以下四个主题：凸性与不变量，哈密顿动力学中的逼近，对称性与分支，以及非线性流形上的守恒数值算法。这项拟议的研究在一定程度上是受到海洋动力学中出现的大规模流体流动问题的推动。例如，薄域中的欧拉方程可以用来模拟浅水波。此外，对保守系统的数值模拟可能会导致对各种天气现象进行更准确的模拟。

9503273 Ratiu The proposed research lies in the area of dynamical systems and geometric mechanics. Specifically, the following four topics are proposed: convexity and invariants, approximation in Hamiltonian dynamics, symmetry and bifurcations, and conserving numerical algorithms on nonlinear manifolds. The proposed research is in part motivated by large scale fluid flow problems arising in ocean dynamics. For example, the Euler equations in thin domains can be used to model shallow water waves. Also, numerical simulations of conservative systems may lead to a more accurate modeling of various weather phenomena.