How does the hopf bifurcation appear in the hydrogen atom in a Circularly Polarized (CP) microwave field?

The dynamics of the Rydberg atom in a rotating electric field can be described by a two degree of freedom Hamiltoniandepending on a parameterK. This Hamiltonian has two equilibrium pointsL1andL2. WhileL1is a saddle-center for allvalues ofK, the hyperbolic character ofL2changes from a double center to a complex saddle as the parameterKcrossesa critical threshold, giving rise to the Hopf bifurcation. Here we analyze the dynamics close to this transition.Postprint (author's final draft