Discrete subgroups of Möbius transformations (Q713455)

It is well known that Jörgensen's inequality gives a necessary condition for a nonelementary two generator subgroup of Möbius transformations acting in \(\hat{\mathbb{R}}^{2}\) to be discrete. \textit{G. J. Martin} [Acta Math. 163, No. 3--4, 253--289 (1989; Zbl 0698.20037)] generalized this to \(\hat{\mathbb{R}}^{n}\). In this paper, the author also gives a necessary condition for this group acting in \(\hat{\mathbb{R}}^{n}\) by extending the so-called stable basin theorem, which gives a necessary condition for two generator subgroups of PU(2,1) to be discrete, developed by \textit{A. Basmajian} and \textit{R. Miner} [Invent. Math. 131, No. 1, 85--136 (1998; Zbl 0901.32018)].