Computational Methods and Function Theory 7 (2007), No. 1, 185--203
Copyright Heldermann Verlag 2007
Alan F. Beardon
afb@dpmms.cam.ac.uk , Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, U.K.
Ian Short
ims25@cam.ac.uk , National University of Ireland, Mathematics Department, Maynooth, Ireland.
We examine Van Vleck's Theorem on continued fractions using Möbius transformations and hyperbolic geometry. Möbius transformations can be defined in several dimensions, so we are able to obtain new results related to Van Vleck's Theorem that are valid in many dimensions.
Keywords: Continued fractions, hyperbolic geometry.
MSC 2000: Primary 40A15, 30B70; Secondary 51B10, 51M10.
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