Level curves of a frozen system given by the Hamiltonian (48). The energy levels are plotted in the (Ξ,ξ) plane, freezing the second (slow) degree of freedom at Υ = const.,υ = 0. Panels A)–D) are characterized by the same values of Υ (that is, Ψ₂) as those shown in Fig. 3. The inadmissible region that arises once the Hamiltonian is formulated in terms of action-angle variables (47), is shown in light purple. Otherwise, the color scheme of the curves is the same as that shown in Fig. 3.