Rational approximations for a Hamiltonian System with three degrees of freedom

We develop a new method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. The idea of the method is to express the solution of the nonlinear ODE in the formx=N/Dⁿ, whereN andD are Fourier series andn is an appropriate constant. We apply this method to a galactic potential with three degrees of freedom.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.