Abstract:

We call a point or orbit typical, if the set of accumulation points of the forward orbit, namely its ω-limit set, coincides with that of almost every point in the Julia set. It is an open question, whether there always exists a typical orbit, and related to the question whether the Julia set of a polynamial may have positive measure. We will study this question for the family of functions, whose set of singularities of the inverse is finite, counting multiplicity.