An approach to Mel’nikov theory in celestial mechanics

DOI10.1063/1.533163zbMath0987.70012arXivchao-dyn/9911015OpenAlexW3100442933MaRDI QIDQ2737851

Manuele Santoprete, Giampaolo Cicogna

Publication date: 30 August 2001

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9911015

zbMATH Keywords

chaosthree-body problemtime-dependent perturbationsGyldén problemArnol'd diffusioncritical point located at infinityKepler-type potentialsnonhyperbolic critical pointsPoincaré-Mel'nikov theory

Mathematics Subject Classification ID

Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05)

Related Items

Chaos in black holes surrounded by electromagnetic fields, Anisotropic two-body problem under the Buckingham potential, On the global dynamics of the anisotropic Manev problem, Partial symmetries and dynamical systems, Qualitative analysis of the anisotropic two-body problem under Seeliger's potential, Qualitative analysis of the anisotropic two-body problem with generalized Lennard-Jones potential, Qualitative analysis of the anisotropic two-body problem with relativistic potential, The Kepler problem with anisotropic perturbations

Cites Work

• Topological equivalence of a plane vector field with its principal part defined through Newton polyhedra
• An example of bifurcation to homoclinic orbits
• Homoclinic orbits and oscillation for the planar three-body problem
• Melnikov method and transversal homoclinic points in the restricted three-body problem
• Triple collision in the collinear three-body problem
• Singularities of vector fields on the plane
• Arnold diffusion and oscillatory solutions in the planar three-body problem
• Bifurcation from heteroclinic orbits with semi-hyperbolic equilibria
• The existence of transverse homoclinic points in the Sitnikov problem
• Melnikov potential for exact symplectic maps
• A geometric criterion for positive topological entropy
• Arnol'd diffusion in the elliptic restricted three-body problem
• Simultaneous equilibrium and heteroclinic bifurcation of planar vector fields via the Melnikov integral
• Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
• Invariant manifolds for a class of parabolic points
• Chaos in the Gyldén problem