Mathematical Sciences: Topics in Dynamical Systems and Smooth Ergodic Theory

主要研究者将分析双曲动力系统和负曲率紧致黎曼流形的相关问题。具体来说，他将研究稳定和不稳定叶的分类、可微性和规律性。其他的研究方向包括对外部参数全局不变量的刚性和正则性的研究。这个项目涉及数学研究的三个领域。动力系统研究的是连续函数多次重复迭代后点的走向。遍历论理论家问的是，在许多这样的迭代中，大多数点（而不是所有点）都去了哪里。黎曼几何关注的是这些点所在的基底空间的曲率和其他方面。首席研究员将分析几个问题，这些问题源于同时应用这三个领域的理论的尝试。

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.