Mathematical Sciences: Topics in Dynamical Systems and Smooth Ergodic Theory

首席研究员将分析相关的 关于双曲动力系统和紧 负曲率黎曼流形。 他特别 将研究分类、可区分性和 稳定和不稳定叶理的规律性。 其他方向 研究包括刚性和规律性的调查， 关于外部参数的全局不变量。 该项目涉及三个数学研究领域。 动力学系统是研究点在经过许多 连续函数的重复迭代。 遍历理论家 问哪里大多数，但不是所有，点去下许多这样的 迭代 黎曼几何关注的是 曲率和基础空间的其他方面， 分数被拿走了。 首席研究员将分析 几个问题，源于试图应用理论， 这三个领域同时出现

The principal investigator will analyze interrelated problems concerning hyperbolic dynamical systems and compact Riemannian manifolds of negative curvature. Specifically, he will investigate the classification, differentiability, and regularity of stable and unstable foliations. Other directions of research include investigations of rigidity and regularity of global invariants with respect to external parameters. This project involves three areas of mathematical research. Dynamical systems is the study of where points go after many repeated iterations of a continuous function. Ergodic theorists ask where most, but not all, points go under many such iterations. And Riemannian geometry is concerned with the curvature and other aspects of the base space from which these points are taken. The principal investigator will analyze several problems which stem from attempts to apply theories from all three of these areas at once.