The meromorphic non-integrability of the three-body problem

DOI10.1515/crll.2001.061zbMath1001.70006arXivmath/0009218OpenAlexW2149392962MaRDI QIDQ2755159

Alexei Tsygvintsev

Publication date: 8 November 2001

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0009218

zbMATH Keywords

variational equationsmeromorphic first integralLagrangian parabolic orbitsmeromorphic non-integrabilityplane three-body problem

Mathematics Subject Classification ID

Three-body problems (70F07) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07)

Related Items (19)

Non-integrability of the equal mass \(n\)-body problem with non-zero angular momentum ⋮ Non-integrability of the three-body problem ⋮ Non-integrability of the dumbbell and point mass problem ⋮ Partial integrability of Hamiltonian systems with homogeneous potential ⋮ Non-integrability of the planar elliptic restricted three-body problem ⋮ Complex dynamics of some Hamiltonian systems: nonintegrability of equations of motion ⋮ Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application ⋮ Integrability analysis of the Shimizu-Morioka system ⋮ On certain integrable and superintegrable weight-homogeneous Hamiltonian systems ⋮ Integrability analysis of natural Hamiltonian systems in curved spaces ⋮ Differential Galois obstructions for non-commutative integrability ⋮ A note on algebraic potentials and Morales-Ramis theory ⋮ Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom ⋮ Non-integrability of some few body problems in two degrees of freedom ⋮ On some exceptional cases in the integrability of the three-body problem ⋮ Integrable planar homogeneous potentials of degree \(- 1\) with small eigenvalues ⋮ Non-integrability of the spacial \(n\)-center problem ⋮ Nonintegrability of the reduced planar three-body problem with generalized force ⋮ Differential Galois Theory and Integration

Cites Work

• Differential Galois theory and non-integrability of Hamiltonian systems
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