Computational Methods and Function Theory 1 (2001), No. 1, 235--248
Copyright Heldermann Verlag 2001
Alan F. Beardon
a.f.beardon@pmms.cam.ac.uk, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, U.K.
Given a sequence $f_j$ of analytic maps of the open unit disc $\mathbb{D}$ into itself, we consider conditions that guarantee that the sequence $f_1\circ\cdots\circ f_n$ of compositions converges uniformly on $\mathbb{D}$ to a constant. The proofs are given entirely in terms of two and three-dimensional hyperbolic geometry.
Keywords: Continued fractions, M\"obius maps, hyperbolic geometry, angular derivatives.
MSC 2000: 30D05, 30C80, 30D45.
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