Integration of a generalized Hénon–Heiles Hamiltonian

DOI10.1063/1.1456948zbMath1059.37043arXivnlin/0112030OpenAlexW2070798678MaRDI QIDQ4830776

Micheline Musette, Robert Conte, Caroline Verhoeven

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0112030

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (9)

Completeness of the cubic and quartic Hénon-Heiles hamiltonians ⋮ Integrable Hénon-Heiles hamiltonians: a Poisson algebra approach ⋮ Exact Solutions in the Invariant Manifolds of the Generalized Integrable Hénon–Heiles System and Exact Traveling Wave Solutions of Klein–Gordon–Schrödinger Equations ⋮ Generic hyperelliptic Prym varieties in a generalized Hénon-Heiles system ⋮ An application of the Kowalewski conditions ⋮ Separation coordinates in Hénon-Heiles systems ⋮ Explicit integration of a generic Hénon-Heiles system with quartic potential ⋮ Exact solutions for a class of integrable Hénon–Heiles-type systems ⋮ Construction of Special Solutions for Nonintegrable Systems

Cites Work

• The Hénon-Heiles system revisited
• A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation
• The complete Whittaker theorem for two-dimensional integrable systems and its application
• Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept
• Factorization of operators I. Miura transformations
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• Separability and Lax pairs for Hénon–Heiles system
• A generalized Henon–Heiles system and related integrable Newton equations
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2

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