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

数学科学：分叉理论、哈密顿动力学和李理论中的辛方法

• 批准号: 9503273
• 负责人: Tudor Ratiu
• 金额: $ 18万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503273&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Symplectic; Methods; Bifuration

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.

建议的研究是在动力系统和几何力学领域。具体地说，提出了以下四个主题：凸性和不变量，哈密顿动力学中的近似，对称性和分岔，以及非线性流形上的守恒数值算法。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浪。此外，对保守系统的数值模拟可能导致对各种天气现象的更精确的模拟。