Hong, Sungbok; Kim, Han-Doo Topological characterizations of certain limit points for Möbius groups. (English) Zbl 0997.20046 Bull. Korean Math. Soc. 38, No. 4, 635-641 (2001). The authors give some characterizations of several kinds of limit points in the case of two generator Schottky groups acting on the Poincaré disc \(B^2\). They take \(\Gamma\) to be a discrete subgroup of the group of hyperbolic isometries acting on the Poincaré disc \(B^m\), \(m\geq 2\). Here, the set \(\Lambda(\Gamma)=\Lambda\) denotes the limit set of \(\Gamma\) and \(\text{CH}(\Lambda)\) denotes the convex hull of \(\Gamma\), where \(\Gamma\) is a non-elementary group.A limit point \(p\) is called a Myrberg-Agard density point for \(\Gamma\) if whenever \(\mu\) is an oriented geodesic for \(\Gamma\) and \(\alpha\) is a geodesic ray ending at the point \(p\) in \(\text{CH}(\Lambda)\), there is a sequence of elements \(\{\gamma_i\}\) such that \(\{\gamma_i(\alpha)\}\) converges to \(\mu\) in an oriented sense. With each \(\alpha\), a special sequence \(S(\alpha)\) is associated. With this terminology, the following theorem is obtained as the main result of the work:Theorem: A necessary and sufficient condition for a limit point \(p\) to be a Myrberg-Agard density point is that for every ray \(\alpha\) ending at \(p\), every admissible sequence appears as a sequence of \(S(\alpha)\). Reviewer: Turgut Başkan (Balikesir) MSC: 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) 57M50 General geometric structures on low-dimensional manifolds 57M60 Group actions on manifolds and cell complexes in low dimensions Keywords:concentration points; limit points; two generator Schottky groups; groups of hyperbolic isometries; Poincaré discs; limit sets; Myrberg-Agard density points; oriented geodesics PDFBibTeX XMLCite \textit{S. Hong} and \textit{H.-D. Kim}, Bull. Korean Math. Soc. 38, No. 4, 635--641 (2001; Zbl 0997.20046)