Elliptic solutions in the Hénon-Heiles model

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.