Explicit integrability for Hamiltonian systems and the Painlevé conjecture

DOI10.1063/1.526185zbMath0566.70020OpenAlexW2060637581WikidataQ123129710 ScholiaQ123129710MaRDI QIDQ3681991

Basile Grammaticos, Alfred Ramani, Bernadette Dorizzi

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1063/1.526185

zbMATH Keywords

Painlevé propertyHénon-Heiles systemnon-integrabilitymovable singularitiescounterexamplespolesbranching of solutionssecond integralquadratic in the velocitiestwo-dimensional integrable HamiltoniansZiglin's criterion

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Singularity analysis of a generalised Lagrange system, Linearization on a submanifold of integrable Hamiltonians with polynomial potentials, A class of 1-D gas flows soluble by the inverse scattering transform, Integrable Hamiltonian systems with velocity-dependent potentials, The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability, The weak-Painlevé property as a criterion for the integrability of dynamical systems, On the integrability of the Hamiltonian systems with homogeneous polynomial potentials, Generalized separability for a Hamiltonian with nonseparable quartic potential, Do all integrable equations satisfy integrability criteria?, Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept, Integrability and the Painlevé property for low-dimensional systems, Chaos around the superposition of a monopole and a thick disk, Symmetries of Hamiltonian systems with two degrees of freedom, Integrability and orbits in quartic polynomial potentials

Cites Work

• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• Analytic structure of the Henon–Heiles Hamiltonian in integrable and nonintegrable regimes