25 Oct 2006; Mat-Nat Faculty (UiTø), room U1=A228. Wednesday 10:15-12:00

Eldar Straume (NTNU, Norway)

"An equivariant Riemannian geometric approach to the 3-body problem in celestial mechanics".

A central topic of the 3-body problem in celestial mechanics is to study the global geometric behaviors of various kinds of trajectories of the Newton's equation, with the classical conservation laws as the basic starting point.

In the setting of Jacobi's geometrization of Lagrange's least action principle, this amounts to the study of the global geometry of geodesics in a 6-dimensional Euclidean space equipped with the conformal modification of the metric by a factor of (U+h). Here U is the potential function and h is the fixed total energy . Moreover, the space has a natural SO(3)-action by isometries.

Thus, we study the global geometry of geodesics in a specific SO(3)-equivariant Riemannian manifold (SO(3),M). Such an approach is radically different from the prevailing study of the 3-body problem in the symplectic geometric setting of the Hamilton-Jacobi theory.