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I will present an overview of the family of quadratic rational maps with a 2- periodic superattracting orbit. Many of these maps can be described as the mating of two quadratic polynomials, one of which is the basilica. For this reason, the family has attracted much recent attention, and the parameter space picture is now nearly completely understood. I will survey the known results, with particular emphasis on my own contribution to the topic: the mateability of Siegel quadratic polynomials of bounded type with the basilica polynomial. |
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