Hamiltonians with two degrees of freedom admitting a singlevalued general solution

DOI10.1007/BF02836923zbMath1092.37042arXivnlin/0507012OpenAlexW2057680628MaRDI QIDQ3379089

Robert Conte, Micheline Musette, Caroline Verhoeven

Publication date: 6 April 2006

Published in: Analysis in Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0507012

zbMATH Keywords

Painlevé propertyPainlevé testhyperelliptic functionsHénon-Heiles Hamiltoniantwo degree of freedom Hamiltonians

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear elliptic equations (35J60) Elliptic functions and integrals (33E05)

Cites Work

• Completeness of the cubic and quartic Hénon-Heiles hamiltonians
• The Hénon-Heiles system revisited
• A perturbative Painlevé approach to nonlinear differential equations
• Integrable quartic potentials and coupled KdV equations
• A note on integrable two-degrees-of-freedom Hamiltonian systems with a second integral quartic in the momenta
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Explicit integration of the Hénon-Heiles Hamiltonians 1