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In a general setting of a Hamiltonian system with two degrees of freedom andassuming some properties for the undergoing potential, we study the dynamicsclose and tending to a singularity of the system which in models of $N$-bodyproblems corresponds to total collision. We restrict to potentials that exhibittwo more singularities that can be regarded as two kind of partial collisionswhen not all the bodies are involved. Regularizing the singularities, the totalcollision transforms into a 2-dimensional invariant manifold. The goal of thispaper is to prove the existence of different types of ejection-collisionorbits, that is, orbits that start and end at total collision. Such orbits areregarded as heteroclinic connections between two equilibrium points and aremainly characterized by the partial collisions that the trajectories find ontheir way. The proof of their existence is based on the transversality of2-dimensional invariant manifolds and on the behavior of the dynamics on thetotal collision manifold, both of them are thoroughly described.

Ejection-collision orbits in two degrees of freedom problems in celestial mechanics