Separability and the Birkhoff-Gustavson Normalization of the Perturbed Harmonic Oscillators with Homogeneous Polynomial Potentials

In this paper, separability of the perturbed two-dimensional isotropic harmonic oscillators with homogeneous polynomial potentials is characterized from their Birkhoff-Gustavson (BG) normalization, one of the conventional methods for non-integrable Hamiltonian systems.