Monodromy and nonintegrability in complex Hamiltonian systems

DOI10.1007/BF01054043zbMath0705.58016MaRDI QIDQ917994

David L. Rod, Richard C. Churchill, Alberto Baider

Publication date: 1990

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

integrabilitymonodromycomplex Hamiltonian system

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Connections (general theory) (53C05)

Related Items (11)

Nonintegrability of the classical Zeeman Hamiltonian ⋮ A criterion for non-integrability based on Poincaré's theorem ⋮ Poisson structures on almost complex Lie algebroids ⋮ Group-theoretic obstructions to integrability ⋮ Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom ⋮ Completion of vector fields and the Painlevé property ⋮ Nonintegrability of Bianchi VIII Hamiltonian system ⋮ Holomorphic last multipliers on complex manifolds ⋮ Numerical evidence of nonintegrability of certain Lie-Poisson system ⋮ Nonintegrability of the Dragt-Finn model of magnetic confinement: A Galoisian-group approach ⋮ HOLOMORPHIC SYMPLECTIC AND POISSON STRUCTURES ON THE HOLOMORPHIC COTANGENT BUNDLE OF A COMPLEX LIE GROUP AND OF A HOLOMORPHIC PRINCIPAL BUNDLE

Cites Work

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• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems
• A criterion for the nonexistence of an additional analytic integral in Hamiltonian systems with \(n\) degrees of freedom

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