Quadrature domains and the real quadratic family

Lazebnik, Kirill

doi:10.1090/ecgd/361

Quadrature domains and the real quadratic family
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by Kirill Lazebnik

Conform. Geom. Dyn. 25 (2021), 104-125

DOI: https://doi.org/10.1090/ecgd/361

Published electronically: September 15, 2021

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

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