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


Authors: Kurt Falk and Katsuhiko Matsuzaki
Journal: Conform. Geom. Dyn. 19 (2015), 159-196
MSC (2000): Primary 30F40; Secondary 37F30
DOI: https://doi.org/10.1090/ecgd/279
Published electronically: June 1, 2015
MathSciNet review: 3351952
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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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Additional Information

Kurt Falk
Affiliation: Universität Bremen, FB 3 - Mathematik, Bibliothekstraße 1, 28359 Bremen, Germany
Email: khf@math.uni-bremen.de

Katsuhiko Matsuzaki
Affiliation: Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku, Tokyo 169-8050, Japan
Email: matsuzak@waseda.jp

DOI: https://doi.org/10.1090/ecgd/279
Received by editor(s): May 9, 2014
Published electronically: June 1, 2015
Additional Notes: The authors were supported by JSPS Grant-in-Aid for Scientific Research (B) #20340030
Article copyright: © Copyright 2015 American Mathematical Society