The Inverse Problem of the Birkhoff-Gustavson Normalization of the Perturbed Harmonic Oscillators with Cubic Potentials

Abstract

A new variant of the symbolic computing program ANFER reproduces the deep relation between the Bertrand-Darboux integrability condition (BDIC) for the perturbed harmonic oscillators with homogeneous cubic polynomial potentials (PHOCPs) and with quartic potentials (PHOQPs) which was discovered in the inverse problem for PHOCPs [1].