F. Calogero et Jp. Francoise, HAMILTONIAN CHARACTER OF THE MOTION OF THE ZEROS OF A POLYNOMIAL WHOSE COEFFICIENTS OSCILLATE OVER TIME, Journal of physics. A, mathematical and general, 30(1), 1997, pp. 211-218
A Hamiltonian is explicitly exhibited, whose equations of motion yield
the time evolution of the n zeros, z(j)(t), of a polynomial of degree
n in z, P-n(z, t) = z(n) + Sigma(m=1)(n) c(m)(t)z(n-m), when its coef
ficients c(m)(t) oscillate, c(m)(t) = c(m)(+)exp(i omega(m)t) + c(m)((
-))exp(-i omega(m)t), or evolve in some other Hamiltonian manner.