the boundary-integral approach provides [@PhysRevE.90.022903]. Therefore, Fig. \[fig:HusimiPhaseSpace\] shows one of the high-Q modes as obtained with this method. In Fig. \[fig:Wavenumber-sweeps\] it corresponds to the top of the peak structure located at $n k \approx 58$ as well as the mode depicted in Fig. \[fig:Field-intensities-forPeaks\] (b). The wave intensity shown in the inset illustrates the appearance of nodal lines which in a conventional WGM would be the radial zeros. As seen in Fig. \[fig:Field-intensities-forPeaks\], successive Q-factor peaks at higher $nk$ in Fig. \[fig:Wavenumber-sweeps\] show additional such “radial” nodes, but the chaotic nature of the underlying phase space makes a rigorous classification in terms of radial nodal lines ambiguous.

The Husimi plot in Fig. \[fig:HusimiPhaseSpace\] (b) instead classifies the mode according to the region of phase space by which it is supported – a procedure that is especially useful in this case because there are no stable ray orbits in the regions of the Poincar[é]{} section bounded by the escape conditions. The six-bounce periodic orbit whose manifolds are explored in Fig. \[fig:HusimiPhaseSpace\] (b) is also shown in Fig. \[fig:HusimiPhaseSpace\] (b), colored yellow and red overlaying the Husimi intensity of the wave solution (the two colors belonging to the two opposite 