Mathematical Sciences: Topics in Dynamical Systems and Smooth Erogodic 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。具体来说，他将 研究分类、可微性和规律性 稳定和不稳定的叶理。其他研究方向 包括对全球化刚性和规律性的研究 关于外部参数的不变量。 该项目涉及三个数学研究领域。 动力学系统是研究点在重复运动下的路径的 连续映射的迭代。遍历理论研究了 在多次迭代下大多数点的长期行为。 黎曼几何描述了空间的性质， 点驻留;曲率等量用于 说明.首席研究员将分析几个 这些问题源于试图应用所有理论 其中三个领域。

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 study of the path of points under repeated iterations of a continuous mapping. Ergodic theory studies the long term behavior of most of the points under many iterations. Riemannian geometry describes the nature of the space in which the points reside; quantities such as curvature are used in the description. The principal investigator will analyze several problems which stem from attempts to apply theories from all three of these areas.