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

2010/06/13 by Hee Oh, Oh, Hee
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1006.2590

openalex publication_date 2010/06/13 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

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

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