# Mathematics Colloquia and Seminars

We apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the restricted three-body problem. These phenomena have been of concern to areas such as capture of comets and trajectory design for newer space missions, like Genesis. We show that the invariant manifold structures associated to libration points $L_1,L_2$ and the heteroclinic connections between their periodic orbits are fundamental tools that aid in understanding dynamical channels throughout the solar system.