The role of the unstable equilibrium points in the transfer of matter in galactic potentials

We study the role of the unstable equilibrium points in the transfer of matter in a galaxy using the potential of a rotating triaxial system. In particular, we study the neighbourhood of these points for energy levels and for main model parameters where the zero velocity curves just open and form a bottleneck in the region. For these energies, the transfer of matter from the inner to the outer parts and vice versa starts being possible. We study how the dynamics around the unstable equilibrium points is driven, by performing a partial normal form scheme and by computing the invariant manifolds of periodic orbits and quasi-periodic orbits using the reduced Hamiltonian. In particular, we compute some homoclinic and heteroclinic orbits playing a crucial role. Our results also show that in slow rotating and/or axisymmetric systems the hyperbolic character of the equilibrium points is cancelled, so that no transfer of matter is possible through the bottleneck.