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Dynamics of Schwarz reflections: the mating phenomena

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arxiv 1811.04979 v3 pith:IYJIY4N7 submitted 2018-11-12 math.DS math.CV

Seung-Yeop Lee , Mikhail Lyubich , Nikolai G. Makarov , Sabyasachi Mukherjee This is my paper · ORCID
classification math.DSmath.CV
keywords schwarzanti-holomorphicdynamicalmapsreflectionreflectionsrespectarise
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We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study Schwarz reflection with respect to the deltoid, and Schwarz reflections with respect to the cardioid and a family of circumscribing circles. We describe the dynamical planes of the maps in question, and show that in many cases, they arise as unique conformal matings of quadratic anti-holomorphic polynomials and the ideal triangle group.

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  1. Univalent Polynomials and Hubbard Trees

    math.CV 2019-08 conditional novelty 8.0 of 10

    Extremal univalent polynomials are classified by bi-angled trees and are in canonical bijection with anti-holomorphic polynomials with all critical points fixed.

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