Abstract
We study several classes of holomorphic dynamical systems associated with quadrature domains. Our main result is that real-symmetric polynomials in the principal hyperbolic component of the Mandelbrot set can be conformally mated with a congruence subgroup ofPSL(2,Z)\mathrm {PSL}(2,\mathbb {Z}), and that this conformal mating is the Schwarz function of a simply connected quadrature domain.
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