Pasting together julia sets: A worked out example of mating

Abstract

The operation of "mating" two suitable complex polynomial maps f1 and f2 constructs a new dynamical system by carefully pasting together the boundaries of their filled Julia sets so as to obtain a copy of the Riemann sphere, together with a rational map f1 ╨ f2 from this sphere to itself. This construction is particularly hard to visualize when the filled Julia sets K(fi) are dendrites, with no interior. This note will work out an explicit example of this type, with effectively computable maps from K(f1) and K(f2) onto the Riemann sphere. © A K Peters, Ltd.