Analytic continuation in the case of non-regular dependency on a small parameter with an application to celestial mechanics

DOI10.1016/j.jde.2005.07.027zbMath1091.34024OpenAlexW2056327161MaRDI QIDQ2575599

Jaume Soler, Conxita Pinyol, Josep Maria Cors

Publication date: 5 December 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.07.027

zbMATH Keywords

periodic orbitsanalytic continuation methodrest cited three-body problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Three-body problems (70F07)

Related Items (12)

From the circular to the spatial elliptic restricted three-body problem ⋮ First kind symmetric periodic solutions of the generalized van der Waals Hamiltonian ⋮ Symmetric periodic orbits in the Hamiltonian galactic-tidal models ⋮ Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem ⋮ First kind symmetric periodic solutions and their stability for the Kepler problem and anisotropic Kepler problem plus generalized anisotropic perturbation ⋮ Periodic solutions of the elliptic isosceles restricted three-body problem with collision ⋮ Doubly symmetric periodic orbits around one oblate primary in the restricted three-body problem ⋮ Families of first kind periodic solutions of the spatial and planar elliptic restricted three-body problem with collision ⋮ Searching for periodic orbits of the spatial elliptic restricted three-body problem by double averaging ⋮ Generalized periodic orbits in some restricted three-body problems ⋮ Periodic solutions of symmetric Kepler perturbations and applications ⋮ New families of symmetric periodic solutions of the spatial anisotropic Manev problem

Cites Work

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• Continuation of periodic solutions in three dimensions
• Doubly-symmetric periodic solutions of the spatial restricted three-body problem
• New periodic solutions of the three dimensional restricted problem
• The continuation of periodic orbits from the restricted to the general three-body problem
• A new method of perturbation theory and its application to the satellite problem of celestial mechanics.
• Periodic solutions in the spatial elliptic restricted three-body problem

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