Submitted by ims_edit on Fri, 02/05/2021 - 14:05
preprint-id:
ims18-06
preprint-title:
Dynamics of Schwarz reflections: the mating phenomena
preprint-abstract:
In this paper, 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 a deltoid, and Schwarz reflections with respect to a 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.
arXiv:1811.04979 |
preprint-year:
2018