The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group

Falk, Kurt; Matsuzaki, Katsuhiko

doi:10.1090/ecgd/279

The critical exponent, the Hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
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by Kurt Falk and Katsuhiko Matsuzaki

Conform. Geom. Dyn. 19 (2015), 159-196

DOI: https://doi.org/10.1090/ecgd/279

Published electronically: June 1, 2015

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Abstract:

In this paper we study the relationship between three numerical invariants associated to a Kleinian group, namely the critical exponent, the Hausdorff dimension of the limit set and the convex core entropy, which coincides with the upper box-counting dimension of the limit set. The Hausdorff dimension of the limit set is naturally bounded below by the critical exponent and above by the convex core entropy. We investigate when these inequalities become strict and when they are equalities.

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