Complete reduction of oscillators in resonance p:q

This paper extends to any type of resonance (p:q) the Lissajous transformation that handles the resonance (1:1) in a Hamiltonian composed of two harmonic oscillators. The manifolds of constant energy for such a system an two-dimensional surfaces of revolution that are spheres for the resonance 1:1, spheres pinched once for the resonances (1:q) when 1