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arXiv · 2010.00706

Quadrature Domains and the Real Quadratic Family

Kirill Lazebnik
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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 of $\textrm{PSL}(2,\mathbb{Z})$, and that this conformal mating is the Schwarz function of a simply connected quadrature domain.

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Kirill Lazebnik. 2020-10-01. Quadrature Domains and the Real Quadratic Family. https://arxiv.org/abs/2010.00706

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