Mathematical Sciences: Strange Attractors of Lorenz-Type, Chaos in the Standard Map and Almost-Periodic Linear Equations

首席研究员将研究三个问题， 动力系统领域。 这些涉及几何洛伦兹 从数学推导出的方程组的吸引子 物理学，大值的标准图的结构 参数和无理旋转上的余循环， 具有拟周期系数的薛定谔算子。 动力系统是研究物体如何运动的数学。 洛仑兹微分方程组描述了 三维空间 首席研究员已经证明， 与洛伦兹系统类似的系统表现出混沌行为 并有一个“奇怪的吸引子。“他将扩展技术， 用来找到更广泛的微分吸引子 方程

The principal investigator will study three problems in the area of dynamical systems. These involve geometric Lorenz attractors for systems of equations derived from mathematical physics, the structure of the standard map for large values of the parameter, and cocycles over an irrational rotation and Schrodinger operators with quasi-periodic coefficients. Dynamical systems is the mathematics of how objects move. The Lorenz system of differential equations describes motion in three dimensions. The principal investigator has proven that a systems similar to the Lorenz system displays chaotic behavior and has a "strange attractor." He will extend the techniques used to find this attractor to a wider class of differential equations.