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arXiv · 1605.02098

Hausdorff dimension of limit sets

Laurent Dufloux
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Abstract

We exhibit a class of Schottky subgroups of $\mathbf{PU}(1,n)$ ($n \geq 2$) which we call well-positioned and show that the Hausdorff dimension of the limit set $\Lambda_\Gamma$ associated with such a subgroup $\Gamma$, with respect to the spherical metric on the boundary of complex hyperbolic $n$-space, is equal to the growth exponent $\delta_\Gamma$. For general $\Gamma$ we establish (under rather mild hypotheses) a lower bound involving the dimension of the Patterson-Sullivan measure along boundaries of complex geodesics. Our main tool is a version of the celebrated Ledrappier-Young theorem.

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Laurent Dufloux. 2016-05-06. Hausdorff dimension of limit sets. https://doi.org/10.1007/s10711-017-0240-2

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