Upper left: example of attractor cycle for a D mode with m = 2, ω_p = −3.75 in a solar-like convective envelope (ε = 0.3, η = 0.71). Upper right: same for a DT mode with m = 0, frequency ω_p = 1.68, and anti-solar conical rotation (ε = −0.3); the white dashed line shows the turning surface. Bottom left: illustration of the focusing of the paths of characteristics at the intersection of the turning surface (dashed line) and the outer boundary of the shell (m = 0, ω_p = 2.4, and ε = 0.5). Bottom right: for m = 2, ω_p = −0.126, and ε = −0.90 two turning surfaces exist within the shell, allowing the propagation of characteristics near the equator or the poles but not in between.