Circle packings, kissing reflection groups and critically fixed anti-rational maps

Abstract

In this paper, 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.

arXiv comment49 pages, 14 figures. The last two sections of v1 are moved to the sequel of this paper. Final version, to appear in Forum of Math. Sigma

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Cited by in corpus (6)

• On Dynamical Gaskets Generated by Rational Maps, Kleinian Groups, and Schwarz Reflections
• Combining Rational maps and Kleinian groups via orbit equivalence
• On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
• The Sullivan dictionary and Bowen-Series maps
• On quasiconformal non-equivalence of gasket Julia sets and limit sets
• Combination Theorems in Groups, Geometry and Dynamics