Mathematical Sciences: Dynamics and Mechanics

两位首席研究员将进行动力系统和力学方面的研究。具体地说，他们对动力系统的研究将包括Conley分解定理的一种新方法，因为它同时适用于映射和矢量场，该定理与计算机舍入误差的关系，以及计算周期轨道和同宿轨道的数值方法。另外，经典N体问题的中心构型，三体问题接近三重碰撞和无限大的轨道，以及广义相对论中混沌的发生，都将是相关研究的主题。“动力系统”是运动的数学。自牛顿以来，数学家们一直在努力了解我们太阳系的动力学。一个只有一个太阳和一颗行星的系统相对容易完全理解。但关于拥有两颗或更多行星的系统，仍有许多未解之谜。例如，最近冥王星的轨道被认为是混乱的。土星环中物体的轨道看起来像是编成了辫子。这两位资深研究人员将运用现代混沌动力系统的大量理论来进一步了解这些复杂的运动。在卫星导航和原子内电子轨迹方面的应用比比皆是。

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.