Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond.

Authors: Hee Oh
Subjects: Dynamical Systems
link: http://arxiv.org/abs/1006.2590
Abstract

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