March 06, 2018
10:00 AM - 11:00 AM
|Xavier Jarque, University of Barcelona|
Wandering domains and singular values
The general framework of this talk will be iteration of transcendental maps on the complex plane. The celebrated Sullivan non wandering domains Theorem asserts that for rational iteration all Fatou components are eventually periodic. Later it was shown that quasi-conformal surgery, Sullivan's main ingredient on his proof, could be used to show that, for instance, critically finite transcendental entire maps have the same property. However it was already known that wandering domains are possible in transcendental dynamics. We will present first some previous results and examples on the (non-) existence of wandering domains.
Secondly, we will focus on the relation between wandering domains and the post singular set for transcendental entire or meromorphic maps. Such relation is (well) understood for other Fatou components, but there are few results relating wandering domains and postsingular set. We will present some new results (joint work with K. Baranski, N. Fagella and B. Karpinska) on this direction. For instance, we will see that if the iterates of such domain do not intersect the postsingular set, and the postsingular set lies at a positive distance from the Julia set (in the complex plane) then any sequence of iterates of wandering domains must contain arbitrarily large disks.