Regularity of the scattering trajectories in classical mechanics (Q1111046)

Consider a classical n-particle system with central, repulsive, pairwise interactions among the particles. The class of motions is studied where the different particles have distinct finite asymptotic velocities as \(t\to \infty\). The author establishes a set of 3 conditions which are sufficient to ensure this behaviour. Exponentially or polynomially decaying potentials and many 1-dimensional n-particle problems satisfy these conditions. The possibility of relaxing the conditions and the alternative approaches to the problem are briefly considered.