Painlevé Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped Hénon-Heiles System

Abstract

We consider a modified damped version of Hénon-Heiles system and investigate its integrability. By extending the Painlevé analysis of ordinary differential equations we find that the modified Hénon-Heiles system possesses the Painlevé property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified Hénon-Heiles system. We infer that the modified Hénon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.