The principal investigator will use this award to initiate a research project in the study of infinite entropy billiard systems with a fractal boundary. She will use Bernoulli theory and the theory of Brownian motion to study perturbations of the flow. She will attempt to prove the robustness of the Markovian model and investigate dynamical systems with singularities. 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.
