The two principal investigators will conduct research on dynamical systems and mechanics. Specifically, their investigations into dynamical systems will include a new approach to the Conley decomposition theorem as it applies both to maps and to vector fields, the relation of this theorem to computer round-off error, and numerical methods for computing periodic and homoclinic orbits. In a separate vein, central configurations in the classical problem of N bodies, orbits of the three-body problem passing close to triple collision and infinity, and the occurrence of chaos in general relativity will be subjects of related studies. "Dynamical systems" is the mathematics of movement. Since Newton, mathematicians have strived to understand the dynamics of our solar system. A system with just one sun and one planet is relatively easy to fully understand. But there remain many unsolved mysteries about systems which have two or more planets. Recently for example, the orbit of the planet Pluto has been thought to be chaotic. And the orbits of objects in Saturn's rings appear braided. These two senior investigators will bring to bear the massive theory of modern chaotic dynamical systems to further understand these intricate motions. Applications to satellite navigation and to trajectories of electrons within atoms abound.
