From global dynamical models to the Hénon–Heiles potential

Abstract

We present a global non-galactic dynamical model reducing to the Hénon–Heiles potential. Expanding the global model in the vicinity of a circular orbit, we find the potential of a two-dimensional perturbed harmonic oscillator which can give the Hénon–Heiles potential for certain values of the parameters of the global model. Our numerical calculations suggest that the properties of motion in the global model are similar of those displayed by the local model for small as well as for large values of energy. Comparison to previous work is also made.