Periodic solutions of symmetric Kepler perturbations and applications. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Alberti, Angelo; Vidal, Claudio
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 3(2016)
• Page Start: 439
• Page End: 465
• Publication Date: 2016-07-02
• Subjects: Perturbation theory -- Symmetries -- Continuation method -- Delaunay-Poincaré variables -- Circular Solutions; 34C25 -- 34C14; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1204721
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : We investigate the existence of several families of symmetric periodic solutions as continuation of circular orbits of the Kepler problem for certain symmetric differentiable perturbations using an appropriate set of Poincaré-Delaunay coordinates which are essential in our approach. More precisely, we try separately two situations in an independent way, namely, when the unperturbed part corresponds to a Kepler problem in inertial cartesian coordinates and when it corresponds to a Kepler problem in rotating coordinates on ℝ 3 . Moreover, the characteristic multipliers of the symmetric periodic solutions are characterized. The planar case arises as a particular case. Finally, we apply these results to study the existence and stability of periodic orbits of the Matese-Whitman Hamiltonian and the generalized Størmer model.