Speaker : Heinz Hanßmann, RWTH Aachen
A rigid body with three equal moments of inertia is moving in a weak nonlinear force field with potential . Next to the -symmetry about the vertical axis and a further -symmetry introduced by normalisation, there is a discrete symmetry due to a special choice of the mass distribution. The continuous symmetries allow to reduce to a one-degree-of-freedom problem, which exhibits bifurcations related to the elliptic umbilic catastrophe. This bifurcation carries over from the integrable approximation to the original system.