Painlevé resonances versus Kowalevski exponents: Some exact results on singularity structure and integrability of dynamical systems

DOI10.1007/BF00046688zbMath0631.70012OpenAlexW1978926443MaRDI QIDQ1094895

Haruo Yoshida, Basile Grammaticos, Alfred Ramani

Publication date: 1987

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00046688

zbMATH Keywords

equations of motionZiglin's methodsingularity analysis``weak Painlevé approachanalytic properties of the solutioncomplex time planeintegrability of a systemtheorem on nonintegrabilityYoshida's method

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations, The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability, The first, second and fourth Painlevé equations on weighted projective spaces, Double three-wave interaction of four waves: Lax representations and exact solutions, Systems of Hess-Appel'rot type, Kovalevskaya exponents and the space of initial conditions of a quasi-homogeneous vector field, Poor man’s scaling: XYZ Coqblin–Schrieffer model revisited

Cites Work

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• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• Hamiltonians with high-order integrals and the ‘‘weak-Painlevé’’ concept
• The Painlevé property for partial differential equations
• Construction of new integrable Hamiltonians in two degrees of freedom
• Necessary condition for the existence of algebraic first integrals