Resumen de Sierpinski and non-Sierpinski curve Julia sets in families of rational maps
We discuss the dynamics as well as the structure of the parameter plane of certain families of rational maps with few critical orbits. Our paradigm is the family Rt(z) = (1 + (4/27)z3/(1 � z)), with dynamics governed by the behaviour of the postcritical orbit (Rn())n. In particular, it is shown that if escapes (that is, Rn() tends to infinity), then the Julia set of R is a Cantor set, or a Sierpiski curve, or a curve with one or else infinitely many cut-points; each of these cases actually occurs.
