Prescribed energy periodic solutions of Kepler problems with relativistic corrections

2023/03/01 by Boscaggin, Alberto, Dambrosio, Walter, Feltrin, Guglielmo · 1 citation
#34C25 #70H08 #70H12 #83A05 #83C10 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.00336

Abstract

We consider two different relativistic versions of the Kepler problem in the plane: the first one involves the relativistic differential operator, the second one involves a correction for the usual gravitational potential due to Levi-Civita. When a small external perturbation is added into such equations, we investigate the existence of periodic solutions with prescribed energy bifurcating from periodic invariant tori of the unperturbed problems. Our main tool is an abstract bifurcation theory from periodic manifolds developed by Weinstein, which is applied in the case of nearly integrable Hamiltonian systems satisfying the usual KAM isoenergetic non-degeneracy condition.

Cited by

• Bifurcation from periodic solutions of central force problems in the three-dimensional space

Related

• Nearly-circular periodic solutions of perturbed relativistic Kepler problems: the fixed-period and the fixed-energy problems
• Periodic solutions to relativistic Kepler problems: a variational approach
• Periodic solutions to a perturbed relativistic Kepler problem
• Bifurcation of closed orbits of Hamiltonian systems with application to geodesics of the Schwarzschild metric
• Relative periodic solutions in spatial Kepler problem with symmetric perturbation