SYMMETRY METHODS IN COLLISIONLESS MANY-BODY PROBLEMS

We formulate an appropriate symmetry context for studying periodic sol utions to equal-mass many-body problems in the plane and 3-space. In a technically tractable but unphysical case (attractive force a smooth function of squared distance, bodies permitted to coincide) we apply t he equivariant Moser-Weinstein Theorem of Montaldi et al. to prove the existence of various symmetry classes of solutions. In so doing we ex poit the direct product structure of the symmetry group and use recent results of Dionne et al. on 'C-axial' isotropy subgroups. Along the w ay we obtain a classification of C-axial subgroups of the symmetric gr oup. The paper concludes with a speculative analysis of a three-dimens ional solution to the 2n-body problem found by Davies el al. and some suggestions for further work.