Integrals in involution for groups of linear symplectic transformations and natural mechanical systems

DOI10.1007/BF02482407zbMath0995.37042MaRDI QIDQ5930956

S. L. Ziglin

Publication date: 21 October 2002

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

zbMATH Keywords

\(n\)-body problemintegral of a motionnatural mechanical system

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) (n)-body problems (70F10)

Related Items (5)

Non-integrability of the equal mass \(n\)-body problem with non-zero angular momentum ⋮ Non-integrability of the three-body problem ⋮ A note on algebraic potentials and Morales-Ramis theory ⋮ Non-integrability of Gross-Neveu systems ⋮ Nonintegrability of the reduced planar three-body problem with generalized force

Cites Work

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• 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
• A criterion for the nonexistence of an additional analytic integral in Hamiltonian systems with \(n\) degrees of freedom
• Oscillatory solutions in the planar restricted three-body problem
• Final motions in the three-body problem and symbolic dynamics
• Differential Galois theory and non-integrability of Hamiltonian systems

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