A class of periodic solutions of the \(N\)-body problem

DOI10.1007/BF00053047zbMath0684.70006MaRDI QIDQ1825695

Vittorio Coti Zelati

Publication date: 1989

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

zbMATH Keywords

N-body problemsmall parameter methodcircular solutionsmultiplicity of T-periodic solutions

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) (n)-body problems (70F10) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (17)

Nonsymmetric ground states of symmetric variational problems ⋮ Some existence results on periodic and generalized periodic solutions for singular hamiltonian systems ⋮ Multiple closed orbits of fixed energy for \(N\)-body-type problems with gravitational potentials ⋮ Non-simultaneous collision periodic solutions for \(N\)-body problems ⋮ Critical points and nonlinear variational problems ⋮ Geometric characterizations for variational minimization solutions of the 3-body problem ⋮ Geometric characterization for variational minimization solutions of the 3-body problem with fixed energy ⋮ Morse index properties of colliding solutions to the \(N\)-body problem ⋮ Multiple closed orbits for perturbed Keplerian problems ⋮ Geometric characterizations for variational minimization solutions of the 3-body problem ⋮ Symmetry groups of the planar three-body problem and action-minimizing trajectories ⋮ Periodic solutions to some \(N\)-body type problems: The fixed energy case ⋮ Collisionless periodic solutions to some three-body problems ⋮ Multiple geometrically distinct closed noncollision orbits of fixed energy for N-body type problems with strong force potentials ⋮ Periodic solutions for N-body type problems ⋮ Multiple closed orbits for N-body-type problems ⋮ Minimization properties of Hill's orbits and applications to some \(N\)-body problems

Cites Work

• Symmetry breaking in Hamiltonian systems
• Perturbation of Hamiltonian systems with Keplerian potentials
• A Minimizing Property of Keplerian Orbits
• Periodic solutions of the N-body problem
• Unnamed Item

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