The Poincaré exponent and the dimensions of Kleinian limit sets

2021/08/11 by Fraser, Jonathan M.
#28A80 #30F40 #Dynamical Systems (math.DS) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2108.05408

Abstract

We provide a proof of the (well-known) result that the Poincaré exponent of a non-elementary Kleinian group is a lower bound for the upper box dimension of the limit set. Our proof only uses elementary hyperbolic and fractal geometry.

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