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

首席研究员将研究动力系统领域的三个问题。这包括数学物理推导出的方程组的几何洛伦兹吸引子，参数大值的标准映射的结构，非理性旋转上的环和准周期系数的薛定谔算子。动力系统是物体如何运动的数学。洛伦兹微分方程组描述三维运动。首席研究员已经证明，一个类似于洛伦兹系统的系统表现出混乱的行为，并有一个“奇怪的吸引子”。他将把找到这个吸引子的方法扩展到更广泛的微分方程中。

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.