%0 Journal Article
%T Outer compositions of hyperbolic/loxodromic linear fractional transfomations
%A John Gill
%J International Journal of Mathematics and Mathematical Sciences
%D 1992
%I Hindawi Publishing Corporation
%R 10.1155/s016117129200108x
%X It is shown, using classical means, that the outer composition of hyperbolic or loxodromic linear fractional transformations {fn}, where fn ¡é   ¡¯f, converges to    ¡À, the attracting fixed point of f, for all complex numbers z, with one possible exception, z0. I.e.,Fn(z):=fn ¡é    fn ¡é   ¡¯1 ¡é     ¡é ? | ¡é    f1(z) ¡é   ¡¯   ¡ÀWhen z0 exists, Fn(z0) ¡é   ¡¯   2, the repelling fixed point of f. Applications include the analytic theory of reverse continued fractions.
%K linear fractional transformations
%K continued fractions
%K fixed points.
%U http://dx.doi.org/10.1155/S016117129200108X