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

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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.

    Original languageEnglish
    Pages (from-to)159-196
    Number of pages38
    JournalConformal Geometry and Dynamics
    Volume19
    Issue number8
    DOIs
    Publication statusPublished - 2015

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    Kleinian Groups
    Limit Set
    Hausdorff Dimension
    Critical Exponents
    Entropy
    Box-counting Dimension
    Equality
    Invariant

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

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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.",
    author = "Kurt Falk and Katsuhiko Matsuzaki",
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