REMARKS ON HAUSDORFF DIMENSIONS FOR TRANSIENT LIMIT SETS OF KLEINIAN GROUPS
REMARKS ON HAUSDORFF DIMENSIONS FOR TRANSIENT LIMIT SETS OF KLEINIAN GROUPS
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关于Kleinian群瞬态极限集Hausdorff维数的评述
DOI：
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发表时间：
2004
期刊：
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通讯作者：
B. Stratmann
中科院分区：
文献类型：
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作者：
K. Falk;B. Stratmann
在本文中，我们研究克莱因群的正规子群以及差异群（d 群），即收敛指数严格小于极限集的豪斯多夫维数的克莱因群。我们证明 d 群的极限集总是包含一系列分形子集，每个分形子集包含径向极限点的集合，并且具有严格小于整个极限集的豪斯多夫维数的豪斯多夫维数。然后我们考虑任意非初等克莱因群 H 的正规子群 G，并证明 G 的收敛指数自下而上受 H 收敛指数一半的限制。最后，我们讨论 d 群的各种例子。
In this paper we study normal subgroups of Kleinian groups as well as discrepancy groups (d-groups), that are Kleinian groups for which the exponent of convergence is strictly less than the Hausdorff dimension of the limit set. We show that the limit set of a d-group always contains a range of fractal subsets, each containing the set of radial limit points and having Hausdorff dimension strictly less than the Hausdorff dimension of the whole limit set. We then consider normal subgroups G of an arbitrary non-elementary Kleinian group H, and show that the exponent of convergence of G is bounded from below by half of the exponent of convergene of H. Finally, we give a discussion of various examples of d-groups.