TY - JOUR
T1 - The critical exponent, the hausdorff dimension of the limit set and the convex core entropy of a Kleinian group
AU - Falk, Kurt
AU - Matsuzaki, Katsuhiko
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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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U2 - 10.1090/ecgd/279
DO - 10.1090/ecgd/279
M3 - Article
AN - SCOPUS:84980022860
SN - 1088-4173
VL - 19
SP - 159
EP - 196
JO - Conformal Geometry and Dynamics
JF - Conformal Geometry and Dynamics
IS - 8
ER -