Outer compositions of hyperbolic/loxodromic linear fractional transfomations

John Gill

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-4

Abstract:

It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations { f n } , where f n → f , converges to α , the attracting fixed point of f , for all complex numbers z , with one possible exception, z 0 . I.e., F n ( z ) : = f n ∘ f n − 1 ∘ … ∘ f 1 ( z ) → α When z 0 exists, F n ( z 0 ) → β , the repelling fixed point of f . Applications include the analytic theory of reverse continued fractions.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:210145

DOI: 10.1155/S016117129200108X

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