Mathematical Sciences: Chaotic Solutions of the n-Body Problem

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The principal investigator will continue his research on singularities of the n-body problem, especially the non-collision singularities and the relation between collision singularities and non-collision singularities. He will also work on some special solutions of the n-body problem which arise from an analysis of the final evolution of the gravitational system. This award will support research in the general area of dynamical systems. A process which is very simple and easy to understand locally can become extremely complicated, nonlinear, and difficult to analyze globally. Dynamical systems is the study of this local to global relationship. Many physical systems can best be modeled using this area of mathematics including fluid flow and turbulence, complex biological systems, mechanical systems, and chemical reactions.