Mathematical Sciences: The Dynamics of Singular Reduction and SubRiemannian Geometry

主要研究人员将探索各种不同的 平衡点和定常点的存在性和稳定性的判据 传统机械系统的运动 不存在办法，或不完全了解办法。他们 将试图推导出形式不稳定性 准确地预测了线性不稳定性的存在， 阻尼小。另一个目标是发展一个 系统的稳定性和分岔分析方法 相空间中的对称态 该奖项将支持一般领域的研究， 动力系统一个非常简单和容易的过程， 局部理解会变得非常复杂，非线性， 很难在全球范围内进行分析。动力系统是研究 从本地到全球的关系。许多物理系统可以 最好是用这一领域的数学建模，包括流体 流动和湍流，复杂的生物系统，机械 系统和化学反应。

The principal investigators will explore various variational criteria for the existence and stability of equilibria and steady motions of mechanical systems in contexts where traditional approaches do not exist or are not completely understood. They will try to derive conditions under which formal instability accurately predicts linear instability in the presence of very small damping. Another objective is the development of a systematic approach to the stability and bifurcation analysis of symmetric states in phase space. This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.