The Julia sets of the random iteration of rational functions (Q1203877)

It is a well-known fact that random iteration of a set of contracting affine mappings may be used to generate fractals. The authors study random iteration of a finite set of rational mappings each viewed as a self-mapping of the Riemann sphere. A dichotomy similar to the concept of Julia sets and Fatou sets known from the theory of iterating a single rational function is introduced. Without any proof the authors state several results like ``The Julia set of a finite set of rational functions equals the closure of the set of the repelling fixed points'' or ``The Julia set is a nonempty perfect set''.