Circle packings, kissing reflection groups and critically fixed anti-rational maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
Abstract
Abstract In this article, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of this correspondence, we give complete answers to geometric mating problems for critically fixed anti-rational maps.
Topics & Concepts
Reflection (computer programming)Simple (philosophy)MathematicsPlanarCombinatoricsComputer scienceEpistemologyComputer graphics (images)PhilosophyProgramming languageGeometric and Algebraic TopologyMathematical Dynamics and FractalsAdvanced Combinatorial Mathematics