Dynamical Systems seminar - Docile entire functions

Dates

Wednesday, March 10, 2021 - 14:00 to 15:00

Speaker: James Waterman (University of Liverpool)

Title: Docile entire functions

Several important problems in complex dynamics are centered around the local connectivity of Julia sets of polynomials and of the Mandelbrot set. Importantly, when the Julia set of a polynomial is locally connected, the topological dynamics of the map can be completely described as a quotient of a power map on the circle.

Local connectivity of the Julia set is less significant for transcendental entire functions. Nevertheless, by restricting to a class of transcendental entire functions, known as docile functions, we obtain a similar concept by describing the topological dynamics as a quotient of a simpler disjoint-type map. We will discuss the notion of docile functions, as well as some of their properties. This is joint work with Lasse Rempe.