  A family of systems related to a linear and bilinear evolution of roots of
polynomials in the complex plane is considered. Restricted to the line, the
evolution induces dynamics of the Coulomb charges in external potentials, while
its fixed points correspond to equilibria of charges (or point vortices in
hydrodynamics) in the plane. The construction reveals a direct connection with
the theories of the Calogero-Moser systems and Lie-algebraic differential
operators. A study of the equilibrium configurations amounts in a construction
(bilinear hypergeometric equation) for which the classical orthogonal and the
Adler-Moser polynomials represent some particular cases
