We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the exponent of convergence of the group.
@article{bwmeta1.element.bwnjournal-article-fmv149i1p83bwm,
author = {B. Stratmann and Mariusz Urba\'nski},
title = {The box-counting dimension for geometrically finite Kleinian groups},
journal = {Fundamenta Mathematicae},
volume = {149},
year = {1996},
pages = {83-93},
zbl = {0847.20046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv149i1p83bwm}
}
Stratmann, B.; Urbański, Mariusz. The box-counting dimension for geometrically finite Kleinian groups. Fundamenta Mathematicae, Tome 149 (1996) pp. 83-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv149i1p83bwm/
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