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