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

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

2010-06-14

arxiv.org/abs/1006.2590v1

Mathematics

Dynamical Systems

To appear in the Proceedings of ICM, 2010

Scientific paper

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.

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