PSS at rotation rate Ω/Ω_k = 0.589 with , where θ is the colatitude and k_θ the projection of the wave vector on the line tangent to the r_p(θ) = r_s(θ)−z curve. Two stable islands are embedded in a chaotic region, which is itself surrounded by whispering gallery rays. The different types of rays are color coded, blue: whispering gallery, green: 6-period island, yellow: 2-period island and red: ergodic.