Computational Methods and Function Theory 1 (2001), No. 2, 535--594
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.
It is well-known that a continued fraction may be regarded as a sequence of M\"obius maps. In this partly expository paper we consider continued fractions by examining the action of M\"obius maps in hyperbolic space, and in all dimensions. We obtain a general version of the Stern-Stolz theorem valid in all dimensions, and we draw comparisons between the theory of continued fractions and the theories of discrete groups of M\"obius maps, and complex dynamics.
Keywords: Continued fractions, Möbius maps, complex dynamics, discrete groups, hyperbolic geometry, inversive geometry.
MSC 2000: Primary 40A15; Secondary 30B70, 11J70.
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