Elliptic solutions in the Hénon–Heiles model

Abstract

Equations of motion corresponding to the Hénon–Heiles Hamiltonian are considered. A method enabling one to find all elliptic solutions of an autonomous ordinary differential equation or a system of autonomous ordinary differential equations is described. New families of elliptic solutions of a fourth-order equation related to the Hénon–Heiles system are obtained. A classification of elliptic solutions up to the sixth order inclusively is presented.