In a general setting of a Hamiltonian system with two degrees of freedom and assuming some properties for the undergoing potential, we study the dynamics close and tending to a singularity of the system which in models of N-body problems corresponds to total collision. We restrict to potentials that exhibit two more singularities that can be regarded as two kind of partial collisions when not all the bodies are involved. Regularizing the singularities, the total collision transforms into a 2-dimensional invariant manifold. The goal of this paper is to prove the existence of different types of ejection–collision orbits, that is, orbits that start and end at total collision. Such orbits are regarded as heteroclinic connections between two equilibrium points and are mainly characterized by the partial collisions that the trajectories find on their way. The proof of their existence is based on the transversality of 2-dimensional invariant manifolds and on the behavior of the dynamics on the total collision manifold; both of them are thoroughly described.

在具有两个自由度的哈密顿系统的一般设置中，并假设经历的潜力有一些属性，我们研究动力学接近并趋向于系统的奇异性，在N体问题的模型中对应于完全碰撞. 我们限制为表现出两个以上奇点的势能，当并非所有物体都涉及时，这些奇点可以被视为两种部分碰撞。正则化奇点，总碰撞转化为二维不变流形。本文的目的是证明不同类型的抛射-碰撞轨道的存在，即以完全碰撞开始和结束的轨道。这种轨道被认为是两个平衡点之间的异宿连接，其主要特征是轨迹在途中发现的部分碰撞。它们存在的证明是基于二维不变流形的横向和总碰撞流形上的动力学行为；他们都被彻底描述。