Upper left: example of attractor cycle for a D mode with m = 2, ωp = −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 ωp = 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, ωp = 2.4, and ε = 0.5). Bottom right: for m = 2, ωp = −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.
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