On the meromorphic non-integrability of some \(N\)-body problems

DOI10.3934/dcds.2009.24.1225zbMath1167.37345OpenAlexW1983800663MaRDI QIDQ833276

Juan J. Morales-Ruiz, Sergi Simon

Publication date: 12 August 2009

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2009.24.1225

zbMATH Keywords

differential algebra\(N\)-body problemsdynamical systems in classical and celestial mechanicsobstructions to integrability (nonintegrability criteria) in Hamiltonian systems

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Dynamical systems in classical and celestial mechanics (37N05) Differential algebra (12H05) (n)-body problems (70F10) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items

Non-integrability of the equal mass \(n\)-body problem with non-zero angular momentum ⋮ Non-integrability of the three-body problem ⋮ Partial integrability of Hamiltonian systems with homogeneous potential ⋮ A note on algebraic potentials and Morales-Ramis theory ⋮ Non-integrability of some few body problems in two degrees of freedom ⋮ Weak-Painlevé property and integrability of general dynamical systems ⋮ Integrable planar homogeneous potentials of degree \(- 1\) with small eigenvalues ⋮ Group analysis of non-autonomous linear Hamiltonians through differential Galois theory ⋮ Nonintegrability of the reduced planar three-body problem with generalized force ⋮ Conditions and evidence for non-integrability in the Friedmann-Robertson-Walker Hamiltonian ⋮ Differential Galois Theory and Integration ⋮ Third order integrability conditions for homogeneous potentials of degree −1