Painlevé analysis, Prelle-Singer approach, symmetries and integrability of damped Hénon-Heiles system

We consider a modified damped version of Henon-Heiles system and investigate its integrability. By extending the Painleve analysis of ordinary differential equations we find that the modified Henon-Heiles system possesses the Painleve 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 Henon-Heiles system. We infer that the modified Henon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.