• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.253-258
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• 1996

For a nonelementary discrete group $\Gamma$ of hyperbolic isometries acting on $B^m(m\geq2)$, we give a topological characterization of conical limit points using admissible pairs.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.77-86
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• 1997

Let $\Gamma$ be a discrete subgroup of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$. The discrete group $\Gamma$ acts properly discontinously in $B^m$, and acts on $\partial B^m$ as a group of conformal homemorphisms, but need not act properly discontinously on $\partial B^m$.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.223-228
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• 1993

In this paper, we use the Patterson-Sullivan measure and results of [H] to show that for a nonelementary discrete group of divergence type, the conical limit set .LAMBDA.$_{c}$ has positive Patterson-Sullivan measure. The definition of the Patterson-Sullivan measure for groups of divergence type is reviewed in section 2. The Patterson-Sullivan measure can also be defined for groups of convergence type and the details for that case can be found in [N]. Necessary definitions and results from [H] are given in section 3, and in section 4, we prove our main result.t.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.945-950
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• 1994

Although the study of the limit points of discrete groups of M$\ddot{o}$bius transformations has been a fertile area for many decades, there are some very natural topological properties of the limit points which appear not to have been previously examined. Let $\Gamma$ be a nonelementary discrete group of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$, and let $p \in \partial B^m$ be a limit point of $\Gamma$. By a neighborhood of p, we will always mean an open neighborhood of p in $\partial B^m$.