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Continued Fractions, Discrete Groups and Complex Dynamics

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Abstract

It is well-known that a continued fraction may be regarded as a sequence of Möbius maps. In this partly expository paper we consider continued fractions by examining the action of Möbius 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 Möbius maps, and complex dynamics.

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    Alan F. Beardone

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Beardone, A.F. Continued Fractions, Discrete Groups and Complex Dynamics. Comput. Methods Funct. Theory 1, 535–594 (2001). https://doi.org/10.1007/BF03321006

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