Pair Collision Transition Operators Of The Three-Body Problem On A Line

The system of three gravitating particles on a line is considered. The forward and backward expansions of the solutions in the Taylor series are used for numerical study of the problem. On the basis of the description of the solutions in the vicinity of pair collision points the pair collision transition operators are introduced. The dynamical problem is reduced to the study of the 2D-maps in the space of free parameters of the system in the vicinity of pair collision points. The first results of the computer simulations are presented.