The Hénon-Heiles system as part of an integrable system in five unknowns with three constants of motions

2014/01/15 by A. Lesfari, Lesfari, A.
Mathematics · Physics and Astronomy · #37J35 #70H06 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math.AG #msc:37J35 #msc:70H06 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1401.3575

arxiv created 2014/01/15 · openalex publication_date 2014/01/15 · arxiv updated 2014/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we construct a new completely integrable system. This system is an instance of a master system of differential equations in 5 unknowns having 3 quartics constants of motion.We find via the Painlevé analysis the principal balances of the hamiltonian field defined by the hamiltonian. Consequently, the system in question is algebraically integrable. A careful analysis of this system reveals an intimate rational relationship with a special case of the well known Hénon-Heiles system. The latter admits asymptotic solutions with fractional powers in t and depending on 3 free parameters. As a consequence, this system is algebraically completely integrable in the generalized sense.

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