Abstract
In this paper, we characterize those external rays that land on the bounded Fatou components of hyperbolic and parabolic quadratic maps. For those maps not in the main cardioid of the Mandelbrot set, we prove that the arguments of these rays form a Cantor subset of the circle at infinity. Our techniques involve both the orbit portraits of Goldberg and Milnor that relate the dynamic and parameter planes and the Thurston theory of laminations for quadratic maps.
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