C1 non-integrability of a hydrogen atom in a circularly polarized microwave field

Abstract

Abstract:Barrabés et al. [Physica D, 241(4), 333-349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the 1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool. PACS

On the Periodic Auto–Oscillations of an Electric Circuit with Periodic Imperfections on Its Variables

“…For doing this we shall use the averaging theory of dynamical systems, see Appendix for more details on it. We have been inspired by other works where these techniques have been used for studying other perturbed dynamics problems, see for instance [2,3,4,5,6,7,8,9,10].…”