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

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

2011-06-22

arxiv.org/abs/1106.4409v3

Mathematics

Complex Variables

Included connections to porosity and the box-counting (or Minkowski) dimension; did minor corrections

Scientific paper

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. 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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