Novel solvable many-body problems

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations motion Newtonian type (“acceleration equals forces”) which determine the points in complex plane. These models solvable, namely their configuration at any time can be obtained from initial data algebraic operations, amounting to determination zeros a known time-dependent polynomial independent variable z. Some these multiply periodic, isochronous or asymptotically isochronous; others display scattering phenomena.