Conditions for the total scattering of a system of bodies in relativistic dynamics with allowance for the aftereffect

The paper examines infinite motions of N bodies when the distance between each pair of bodies tends with time to infinity. This problem is considered in the case of functional-differential equations of motion of a general kind which include equations of motion in the weak field approximation of general relativity and in relativistic electrodynamics (without self-interaction). Sufficient conditions of total scattering are obtained along with estimates of solution behavior.