Chaos in the Gyldén problem

DOI10.1063/1.532663zbMath0944.70011OpenAlexW2023096003MaRDI QIDQ4701580

Dan Şelaru, Florin Nicolae Diacu

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532663

zbMATH Keywords

perturbed Kepler problemGyldén problemMelnikov integralMcGehee transformationshift automorphismplanar periodic perturbationsPoincaré-Melnikov-type criterion

Mathematics Subject Classification ID

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Two-body problems (70F05) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (5)

Chaotic dynamics of the Kepler problem with oscillating singularity ⋮ Particle dynamics in a Maxwell's ring-type configuration with a radiating central primary ⋮ An approach to Mel’nikov theory in celestial mechanics ⋮ A practical use of the Melnikov homoclinic method ⋮ The Kepler problem with anisotropic perturbations

Cites Work

• Melnikov method and transversal homoclinic points in the restricted three-body problem
• Triple collision in the collinear three-body problem
• Arnold diffusion and oscillatory solutions in the planar three-body problem
• Transition tori in the five-body problem
• Arnol'd diffusion in the elliptic restricted three-body problem
• A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
• The secular acceleratons in Gylden's problem
• Melnikov's method and averaging
• Averaging and Chaotic Motions in Forced Oscillations
• Asymptotic expansions in the perturbed two-body problem with application to systems with variable mass

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