To and fro motion for the hydrogen atom in a circularly polarized microwave field

- Regularization of the equations of motion.
- Mechanism that explains to and fro motion.
- Computation of families (and bifurcations) of ECO.
- Description of the dynamics of the CP problem in a global sense.

We study the problem of the hydrogen atom interacting with a circularly polarized microwave field, and more specifically, we focus on the so called to and fro motion, that is, the erratic trajectories described by the electron making several large distance excursions and close passages to the nucleus. The skeleton of such trajectories is based on the so called ejection-collision orbits (ECO), that is, orbits ejected from the nucleus, describing several far/close passages to the origin and finally colliding with it. The computation and continuation of families of ECO, as well as their bifurcations is analysed, and finally the consequences of such orbits to explain to and from motion as well as ionization of an electron by the external field are also described.