Abstract:

I'll summarize some (old and well known) results about the constant limit functions for points in a wandering domain (that is, a non-periodic Fatou component) and its relationship with the post--singular set. I will obtain some interesting, well known corollaries. I will also present a result from L. Rempe and H. Mihaljevic-Brant on the non existence of wandering domains for certain maps of bounded type. Finally I will discuss (briefly... since, to tell the truth, I do not understand quite well...) a recent result of C. Bishop which allows him to produce examples of entire maps with a controlled number of critical values (images of critical points). From this, he is able to give the first example of a wandering domain for a bounded type map.