Some homoclinic phenomena in the three-body problem
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Publication:1145517
DOI10.1016/0022-0396(80)90109-6zbMath0445.70005OpenAlexW2042880393MaRDI QIDQ1145517
Publication date: 1980
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-0396(80)90109-6
Poincaré mapBernoulli shifttransversal homoclinic pointhomoclinic phenomenarestricted collinear problem
Three-body problems (70F07) Dynamical systems in classical and celestial mechanics (37N05) General models, approaches, and methods in mechanics of particles and systems (70G99)
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Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near \(L_ 2\) in the restricted three-body problem ⋮ Arnol'd diffusion in the elliptic restricted three-body problem ⋮ Secular instability in the three-body problem ⋮ Measure of the exponential splitting of the homoclinic tangle in four-dimensional symplectic mappings ⋮ Conservative homoclinic bifurcations and some applications ⋮ Integrability of Hamiltonian systems and differential Galois groups of higher variational equations ⋮ Non-integrability of Hamiltonian systems through high order variational equations: summary of results and examples ⋮ Symbolic dynamics in the planar three-body problem ⋮ Oscillatory orbits in the restricted planar four body problem ⋮ Melnikov method and transversal homoclinic points in the restricted three-body problem ⋮ Oscillatory orbits in the restricted elliptic planar three body problem ⋮ Dynamics and chaos in the elliptic isosceles restricted three-body problem with collision ⋮ Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem ⋮ Oscillatory motions for the restricted planar circular three body problem ⋮ Symbolic dynamics in the restricted elliptic isosceles three body problem ⋮ Asymptotic orbits in the \((N+1)\)-body ring problem ⋮ Oscillatory solutions in the planar restricted three-body problem ⋮ Chebyshev–Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications ⋮ Oscillatory motions and parabolic manifolds at infinity in the planar circular restricted three body problem
Cites Work
- 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
- QUASIRANDOM DYNAMICAL SYSTEMS. III QUASIRANDOM OSCILLATIONS OF ONE-DIMENSIONAL OSCILLATORS
- ON MOULTON'S ORBITS IN THE RESTRICTED PROBLEM OF THREE BODIES
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