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Published online by Cambridge University Press: 24 October 2008
Let D be the unit disc in the complex plane ℂ with centre 0 and let ∂D be its boundary. By Möb (D) we denote the group of all Möbius transformations which leave D invariant. A Fuchsian group G acting on D is a discrete subgroup of Möb (D). The limit set of G is in ∂D. We decompose ∂D into the following three disjoint sets: