The principal investigators will explore various variational criteria for the existence and stability of equilibria and steady motions of mechanical systems in contexts where traditional approaches do not exist or are not completely understood. They will try to derive conditions under which formal instability accurately predicts linear instability in the presence of very small damping. Another objective is the development of a systematic approach to the stability and bifurcation analysis of symmetric states in phase space. 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.
