Poincaré Surface of Section (PSS) at the rotation rate Ω/Ω_K = 0.589 for quantum number m = 0. Each dot corresponds to the crossing of an acoustic ray with the equatorial half-plane in the (r/R_eq,k_r/ω) phase space, r being the radial coordinate and k_r the associated momentum. R_eq is the equatorial radius and ω the mode frequency. Red/dark gray denotes a chaotic ray, green/light gray a whispering gallery ray, blue/black a stable island ray (see text). Upper inset is a close-up of the main stable island. (This figure is available in color in the electronic form.)