Periodic orbits in time-dependent planar Stark-Zeeman systems

Abstract: Time-dependent Stark-Zeeman systems describe the motion of an electron attracted by a proton subject to a magnetic and a time-dependent electric field. For instance the study of the dynamics of a gateway around the moon which is subject to the joint attraction of the moon, the earth and the sun leads to time-dependent Stark-Zeeman systems. In the time-dependent case there is no preserved energy. Therefore collisions cannot be regularized by blowing up the energy hypersurface. A new regularization technique of blowing up instead of the energy hypersurface the loop space was recently discovered by Barutello, Ortega, and Verzini. In this article we explain how this new regularization technique can be applied to the study of periodic orbits in time-dependent planar Stark-Zeeman systems. Since the regularization by blowing-up the loop space is nonlocal the regularized periodic orbits will not satisfy an ODE anymore but a delay equation.