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

preprint2010arXivOpen access

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 33 manifolds are related. Our results apply to Apollonian circle packings, Sierpinski curves, Schottky dances, etc.

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