On the holonomy group associated with analytic continuations of solutions for integrable systems

DOI10.1007/BF01236284zbMath0762.58015MaRDI QIDQ4009901

Hidekazu Ito

Publication date: 27 September 1992

Published in: [https://portal.mardi4nfdi.de/entity/Q2710393 Boletim da Sociedade Brasileira de Matem�tica] (Search for Journal in Brave)

zbMATH Keywords

Poincaré mapssymplectic manifoldintegrable Hamiltonian systemsholonomy groupRiemann-surface

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) Riemann surfaces (30F99)

Related Items (7)

A criterion for non-integrability based on Poincaré's theorem ⋮ Non-integrability in Hamiltonian mechanics ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Morales-Ramis theorems via Malgrange pseudogroup ⋮ Nonintegrability of Bianchi VIII Hamiltonian system ⋮ A non-integrability test for perturbed separable planar Hamiltonians ⋮ Numerical evidence of nonintegrability of certain Lie-Poisson system

Cites Work

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• A criterion for non-integrability of Hamiltonian systems with nonhomogeneous potentials
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• Geometrical aspects of Ziglin's non-integrability theorem for complex Hamiltonian systems
• Non-integrability of the truncated Toda lattice Hamiltonian at any order
• Convergence of Birkhoff normal forms for integrable systems
• Action-angle coordinates at singularities for analytic integrable systems
• Integrability and non-integrability in Hamiltonian mechanics

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