Flows on Homogeneous Spaces and Diophantine Approximation

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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.