Christof Jung (UNAM, Mexico)
The role of normally hyperbolic invariant manifolds in barred galaxies
We study the dynamics in the rotating frame of a test particle in the gravitational field of a barred galaxy. The effective potential has Lagrange points (which in this case are index 1 saddle points) at the connections between the bar and the spiral arms or the rings. Over these saddle points we find normally hyperbolic invariant manifolds (NHIMs) in the phase space. The spiral arms or the rings run along the projection into the position space of the outer unstable manifolds of the NHIMs. This observation suggests that the formation of the arms or the rings is at least partially triggered by perturbations running along the unstable manifolds of the NHIMs. The NHIMs show a complicated development scenario as function of the energy and of the bar length. We study the NHIM properties by a restriction of the Poincare map to the NHIMs.