Figure 1

Bifurcation diagram of the HOCl molecule for $I_1=1/2$ as a function of $P$ [see Eq. (1)]. The energies of the period orbit [B] characterized by $p_3=q_3=0$ have been subtracted from each energy in order to clarify the plot (see Ref. 15 for details). The critical points of $\mathcal{E}\mathcal{M}$ are represented by solid and dashed lines. Points of the solid lines lift to points or circles in the original phase space, while points of the dashed lines lift to curled tori or bitori. A representation of these two singular tori is also given in this figure. The red dot $C$ is the intersection point of these two lines. The two paths with arrows in black correspond to the bipath used to define the bidromy (see the text). The grey region is the zone where the two leaves of the bifurcation diagram overlap.Reuse & Permissions

Figure 2

Parallel transport of the cell through the vibrational spectrum of HOCl. The energy levels of the upper and lower leaves are, respectively, depicted in blue (full) and red (open) dots. The effective value of $\hslash$ is taken to be 0.5 for the sake of a clearer illustration. The initial cell is broken into two cells when crossing the line of bitori. One of the two cells, the light grey one, belongs to the lower leaf, while the other belongs to the upper leaf. The final cell, the red (medium grey) one, is defined by the addition of the two final cells of the two paths.Reuse & Permissions