Quadrature Domains and the Real Quadratic Family

2020/10/01 by Lazebnik, Kirill · 1 citation
#30C10 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.00706

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 \textrmPSL(2,ℤ), and that this conformal mating is the Schwarz function of a simply connected quadrature domain.

Cited by

• Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groups

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