DYNAMICS OF 2 INTERACTING PARTICLES IN CLASSICAL BILLIARDS

The problem of two interacting particles moving in a d-dimensional bil liard is considered here. A suitable coordinate transformation leads t o the problem of a particle in an unconventional hyperbilliard. A dyna mical map can be readily constructed for this general system, which gr eatly simplifies calculations. As a particular example, we consider tw o identical particles interacting through a screened Coulomb potential in a one-dimensional billiard. We find that the screening plays an im portant role in the dynamical behavior of the system and only in the l imit of vanishing screening length can the particles be considered as bouncing balls. For more general screening and energy values, the syst em presents strong nonintegrability with resonant islands of stability .