Formation of Symmetric Structures in the Dynamics of Repelling Particles

We consider Hamiltonian systems corresponding to the motions of a system of N repelling particles evolving in space under the action deriving from a very long range potential energy; the asymptotic behavior of the system is analysed for the cases U=− ln r and . Only special “asymptotic?shapes” are reached, which may present quite interesting symmetries and correspond to the critical points of a gradient system. The relationships between the original Hamiltonian and the asymptotic gradient system are discussed. Accepted: May 25, 1999