| Abstract: |
| The talk deals with electromagnetic perturbations of a central force problem. The considered differential operator includes, as special cases, the classical one as well as that of special relativity. We investigate whether non-circular periodic solutions of the unperturbed problem can be continued into periodic solutions for small perturbations, both for the fixed-period problem and, if the perturbation is time-independent, for the fixed-energy problem. The proof is based on an abstract bifurcation theorem of variational nature, which is applied to suitable Hamiltonian action functionals. In checking the required nondegeneracy conditions we take advantage of the existence of partial action-angle coordinates as provided by the Mishchenko--Fomenko theorem for superintegrable systems. Physically relevant problems to which our results can be applied are homogeneous central force problems in classical mechanics and the Kepler problem in special relativity. |
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