Existence and Linear Stability of Symmetric Periodic Orbits in the Generalized Planar Stark–Zeeman Problem

The purpose of this paper is to demonstrate the existence of symmetric periodic solutions for a two-dimensional hydrogen atom subject to external electric and magnetic fields. We build upon the analysis of periodic orbits that was initially performed by De Bustos et al. (J Math Phys 53:082701, 2012). In this study, we utilize the symmetry of reflection and an appropriate set of variables to obtain results regarding the existence and stability of periodic solutions. Furthermore, we determine the presence of KAM 2-tori that enclose some of the linearly stable periodic solutions.