Leticia Pardo Simon: Entire functions with unbounded wandering domains

Abstract

In the iteration of transcendental entire functions, one might encounter components of its Fatou set, that is, the locus of stable behaviour, that are not eventually periodic. These are known as wandering domains. Following Baker's first example from 1976, many examples of transcendental entire functions with wandering domains have been provided, and in recent years, with the development of new techniques, much progress on the understanding of bounded wandering domains has been achieved. In this talk, I will describe how functions with unbounded wandering domains, that escape to infinity 'as fast as possible' under iteration, can be constructed. This is based on joint work with A. Glücksam and V. Evdoridou.