076 David Martí-Pete

Wandering domains in transcendental dynamics: topology and dynamics // Abstract: For a transcendental entire or meromorphic function, the Fatou set is the largest open set on which its iterates are defined and form a normal family. A wandering domain is a connected component of the Fatou set which is not eventually periodic. The first example of a transcendental entire function with a wandering domain was constructed by Baker in the 1970s. Wandering domains, which do not exist for rational maps, play an important role in transcendental dynamics and in the last decade there has been a resurgence in their interest. For example, Bishop proved that the Julia sets of transcendental entire functions can have Hausdorff dimension 1 by constructing a function with wandering domains. Wandering domains are very diverse in terms of both their topology (simply connected or multiply connected) and their dynamics (escaping, oscillating or, perhaps, even have bounded orbit). Recently, ...