## Remarks on points of approximation of discrete subgroups of $$U(1,n;\mathbb{C})$$.(English)Zbl 0814.30026

Let $$G$$ be a discrete subgroup of $$U(1,n; \mathbb{C})$$ acting on the complex unit ball $$B^ n$$. Let $$\zeta= (\zeta_ 1, \zeta_ 2,\dots, \zeta_ n)$$ be a limit point of $$G$$. If there exists a sequence $$\{g_ k\}$$ of distinct elements of $$G$$ and a region $$D_ \alpha (\zeta)= \{z= (z_ 1, z_ 2,\dots, z_ n)\in B^ n\mid | 1- \sum_{i=1}^ n \overline {z}_ i \zeta_ i|< \alpha(1- \sum_{i=1}^ n | z_ i|^ 2 )\}$$ such that $$g_ k(0)\in D_ \alpha (\zeta)$$ and $$g_ k(0)\to \zeta$$, then the point $$\zeta$$ is called a point of approximation of $$G$$. We show that a point of approximation of $$G$$ has some similar properties as in Kleinian groups. But in the case where $$n\geq 2$$, an approach to a point of approximation is not necessarily non-tangential. We give an example of a point of approximation to which some orbit converges in the tangential direction.
Reviewer: S.Kamiya (Okayama)

### MSC:

 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 22E40 Discrete subgroups of Lie groups
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### References:

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