Gwyneth Stallard: Dynamical properties of entire functions of small growth
Abstract:
This talk concerns the iteration of transcendental entire functions - in particular, of such functions for which the growth is small and so, in some sense, the resemblance to a polynomial is as close as possible for a transcendental function. We show how the properties of such functions lead to a surprising link between two apparently unrelated conjectures and discuss recent progress on both conjectures. The first conjecture, due to Baker, concerns the components of the Fatou set (the set of points that are stable under iteration). The second conjecture, due to Eremenko, concerns the components of the escaping set (the set of points that tend to infinity under iteration).
This is joint work with Phil Rippon.