Mathematical Sciences: Dynamics and Mechanics

数学科学：动力学和力学

• 批准号: 8906296
• 负责人: Richard McGehee
• 金额: $ 5.16万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8906296&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamics; Mechanics

The two principal investigators will conduct research on dynamical systems and mechanics. Specifically, their investigations into dynamical systems will include a new approach to the Conley decomposition theorem as it applies both to maps and to vector fields, the relation of this theorem to computer round-off error, and numerical methods for computing periodic and homoclinic orbits. In a separate vein, central configurations in the classical problem of N bodies, orbits of the three-body problem passing close to triple collision and infinity, and the occurrence of chaos in general relativity will be subjects of related studies. "Dynamical systems" is the mathematics of movement. Since Newton, mathematicians have strived to understand the dynamics of our solar system. A system with just one sun and one planet is relatively easy to fully understand. But there remain many unsolved mysteries about systems which have two or more planets. Recently for example, the orbit of the planet Pluto has been thought to be chaotic. And the orbits of objects in Saturn's rings appear braided. These two senior investigators will bring to bear the massive theory of modern chaotic dynamical systems to further understand these intricate motions. Applications to satellite navigation and to trajectories of electrons within atoms abound.

两名主要研究人员将进行研究， 动力系统和力学。 具体来说，他们 对动力系统的研究将包括一种新的方法 康利分解定理，因为它既适用于地图 对于向量场，这个定理与计算机的关系 四舍五入误差，以及计算周期和 同宿轨道 在一个单独的静脉中， 经典的N体问题，三体轨道 问题通过接近三重碰撞和无穷大，并且 广义相对论中的混沌现象将成为 相关研究。 “动力系统”是运动的数学。 以来 牛顿，数学家们一直在努力理解 我们的太阳系 一个只有一个太阳和一颗行星的系统 相对容易完全理解。 但仍有许多 关于有两个或更多行星的系统的未解之谜。 例如最近冥王星的轨道 被认为是混乱的。 土星轨道上的物体 环呈编织状。 这两位高级调查员将带来 承载现代混沌动力系统的大规模理论， 进一步理解这些复杂的运动。 应用程序 卫星导航和电子的轨迹 原子比比皆是。