MOBIUS ITERATED FUNCTION SYSTEMS

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Mobius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, in terms of topological, geometric, and dynamical properties, of Mobius iterated function systems that possess an attractor. The paper also includes results on the duality between the attractor and repeller of a Mobius iterated function system.