Dynamics on Geometrically Finite Hyperbolic Manifolds with Applications to Apollonian Circle Packings and Beyond

摘要

We present recent results on counting and distribution of circles in a given circlepacking invariant under a geometrically finite Kleinian group and discuss howthe dynamics of flows on geometrically finite hyperbolic 3 manifolds are related.Our results apply to Apollonian circle packings, Sierpinski curves. Schottkydances, etc.