International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 819-822

Outer compositions of hyperbolic/loxodromic linear fractional transfomations

John Gill

Mathematics Department, University of Southern Colorado, Pueblo 81001, CO, USA

Received 29 July 1991

Copyright © 1992 John Gill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fnf, converges to α, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z):=fnfn1f1(z)αWhen z0 exists, Fn(z0)β, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions.