Flows on Homogeneous Spaces and Diophantine Approximation

小行星9704489 这个项目涉及代数动力系统及其在数论中的应用。关于丢番图近似的许多问题可以用适当的齐次流的轨道的行为来描述。非一般的轨道，如那些避免一个给定的有限集或那些保持有界的特别感兴趣。调查员是继续他的工作逃避集和度量性质的矩阵所产生的丢番图近似。 动力系统在本文中处理系统中的点如何随时间移动，给定一组微分方程（或自然定律）来控制系统。事实证明，在整数方程理论中使用的各种数值近似可以更好地计算，一旦他们在动力系统语言中措辞。

9704489 Kleinbock This project deals with algebraic dynamical systems and their applications to number theory. Many problems concerning diophantine approximations can be cast in terms of the behavior of the orbits of a suitable homogeneous flow. Non-generic orbits such as those avoiding a given finite set or ones that remain bounded are of particular interest. The investigator is to continue his work on escapable sets and metric properties of matrices arising in diophantine approximations. Dynamical systems in the present context deal with how points in a system move over time, given a set of differential equations (or laws of nature) governing the system. It turns out that various numerical approximations used in the theory of integer equations can be better calculated once they are phrased in dynamical systems language.