Elliptic solutions in the Hénon - Heiles model
arXiv:1208.0726
Abstract
Equations of motion corresponding to the Hénon - Heiles system 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.