Mathematical Sciences: Differentiable Dynamical Systems

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The principal investigators will continue work in problems in dynamical systems and differential geometry. Professor Burns will study geodesic flows on Riemannian manifolds of negative curvature and the problem of constructing metrics whose geodesic flow is ergodic. Professor Franks will focus on the dynamics of homeomorphisms of surfaces and in particular, area preserving homeomorphisms. Professor Robinson will focus on the stability conjecture for flows in higher dimensions. He will also continue his study of the bifurcations in the formation of the "Smale horseshoe". 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.