We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian depending on one parameter K>0, which is a perturbation of the standard Kepler problem. The associated Hamiltonian system has two equilibria: L1 (center-saddle for all K) and L2 (center-center for small K and complex-saddle otherwise). Associated to L1 there is a family of Lyapunov periodic orbits that form a normally hyperbolic invariant manifold (NHIM). In this talk, we compute the primary transversal homoclinic orbits to the NHIM (and therefore the associated scattering maps) combining Poincaré-Melnikov methods with numerical methods. It should be noted that the transversality of these homoclinic orbits is exponentially small in K (in analogy with the libration point L3 of the R3BP).

This is a joint work with Mercè Ollé and Juan R. Pacha (Universitat Politècnica de Catalunya).

Zoom link: https://utoronto.zoom.us/j/88134686264 -- Passcode: 452271