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Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond
Published 14 Jun 2010 in math.DS and math.GT | (1006.2590v1)
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.
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