Melnikov method and transversal homoclinic points in the restricted three-body problem
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Publication:1184666
DOI10.1016/0022-0396(92)90149-HzbMath0741.70007MaRDI QIDQ1184666
Publication date: 28 June 1992
Published in: Journal of Differential Equations (Search for Journal in Brave)
Related Items (27)
Arnol'd diffusion in the elliptic restricted three-body problem ⋮ A note on the existence of a Smale horseshoe in the planar circular restricted three-body problem ⋮ The two-body problem with radiation pressure in a rotating reference frame ⋮ Horseshoes and nonintegrability in the restricted case of a spinless axisymmetric rigid body in a central gravitational field ⋮ Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations ⋮ Conservative homoclinic bifurcations and some applications ⋮ GEOMETRY OF HOMOCLINIC CONNECTIONS IN A PLANAR CIRCULAR RESTRICTED THREE-BODY PROBLEM ⋮ The existence of a Smale horseshoe in a planar circular restricted four-body problem ⋮ Non-integrability of the planar elliptic restricted three-body problem ⋮ Destruction of invariant curves in the restricted circular planar three-body problem by using comparison of action ⋮ Unnamed Item ⋮ Stable manifolds associated to fixed points with linear part equal to identity. ⋮ Symbolic dynamics in the planar three-body problem ⋮ Oscillatory orbits in the restricted planar four body problem ⋮ On stochastic sea of the standard map ⋮ Global instability in the restricted planar elliptic three body problem ⋮ Oscillatory orbits in the restricted elliptic planar three body problem ⋮ An approach to Mel’nikov theory in celestial mechanics ⋮ Global existence and singularity of Hill’s lunar problem with strong potential ⋮ Oscillatory motions in restricted \(N\)-body problems ⋮ Oscillatory motions for the restricted planar circular three body problem ⋮ The existence of transversal homoclinic orbits in a planar circular restricted four-body problem ⋮ Chaos in the Gyldén problem ⋮ Invariant manifolds of parabolic fixed points. I: Existence and dependence on parameters ⋮ Chaotic Rotations of a Rigid Ellipsoidal Body Exhibiting Spin-Orbit Misalignment in a Periodic Orbit ⋮ Chaotic orbits in a restricted three-body problem: numerical experiments and heuristics ⋮ Stable curves asymptotic to a degenerate fixed point
Cites Work
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- Lagrangian submanifolds and Hamiltonian systems
- The existence of oscillatory and superhyperbolic motion in Newtonian systems
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Some homoclinic phenomena in the three-body problem
- Parabolic orbits in the planar three body problem
- Homoclinic orbits and oscillation for the planar three-body problem
- Oscillatory solutions in the planar restricted three-body problem
- A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
- Stable and Random Motions in Dynamical Systems
- Heteroclinic Phenomena in the Isosceles Three-Body Problem
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