Akishin P.G, Puzynin I.V., Vinitsky S.I.

Pair collision transition operators for the three-body problem on a line
P.G. Akishin, I.V. Puzynin, S.I. Vinitsky
Joint Institute for Nuclear Research, 141980 Dubna, Russia

A new approach based on the reduction of the dynamical three-body problem on a line to the 2D-maps in the space of parameters has been proposed [1]. The pair collision transition operators (PCTO) given as the 2D-maps on a grid has been constructed on the base of developed hybrid numerical algorithms and detailed description of three-body dynamics in the vicinity of two-body collision points [2]. Making use of spline approximations the fulfillment procedure for the grid PCTO has been developed. It allows to extend the grid PCTO to the continuous parameter domain. The method of PCTO reduces the continuous three-body calculations on the level of trajectories to the discrete time dynamics on the 2D-parameter space and allows to exclude numerical calculations between two-body collisions points. It will give the base for the further investigations of the peculiarities of the complex dynamics of the three-body system on a line. Some results of computer simulation of the problem under consideration are discussed.

1. P.G. Akishin, I.V. Puzynin and S.I. Vinitsky, In: The Proc. of Int. Conf. NDCCS, Zakopane, 7-12 November, 1995, Poland; Acta Physica Polonica, 1996 (to be published).
2. P.G. Akishin, I.V. Puzynin and S.I. Vinitsky, Int. J. Computers Mathematics with Applications, 1996 (to be published).