Dynamic classification of escape time Sierpinski curve Julia sets

For n >= 2, the family of rational maps F lambda(z) = z(n) + lambda/z(n) contains a countably infinite set of parameter values for which all critical orbits eventually land after some number kappa of iterations on the point at infinity. The Julia sets of such maps are Sierpinski curves if kappa >= 3. We show that two such maps are topologically conjugate on their Julia sets if and only if they are Mobius or anti-Mobius conjugate, and we give a precise count of the number of topological conjugacy classes as a function of n and kappa.