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

2024/03/13 by C. Uma Maheswari, Maheswari, C. Uma, N. Muthuchamy +7
Engineering · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2403.08410

openalex publication_date 2024/03/13 · openalex created_date 2024/03/15 · openalex updated_date 2026/08/01

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.

Related

• The Painleve Analysis and Special Solutions for Nonintegrable Systems
• The Hénon-Heiles system as part of an integrable system in five unknowns with three constants of motions
• Vector systems of Painlevé type
• Orbits in the integrable Hénon-Heiles systems
• Non-integrability of a three dimensional generalized Hénon-Heiles system