LMS lectures on Holomorphic Dynamics

We are pleased to announce an online graduate lecture series on Holomorphic Dynamics which will be addressed to PhD students in Mathematics. The series is supported by the London Mathematical Society, and it is organised by our Scheme 3 Holomorphic Dynamics Joint Research Network. This network consists of the Holomorphic Dynamics groups at Imperial College London, The Open University, University of Liverpool and University of Nottingham.

The series will consist of 6 one-hour lectures which will focus on the iteration of entire functions exploring, among other things, some famous fractal Julia sets and the well-known Mandelbrot set. In particular, we will cover the following topics:

• Equicontinuity, normal families, Montel's theorem, Riemann mapping theorem, the Riemann sphere.

• Iteration of polynomials. Definition of the Fatou set and the Julia set for a polynomial. Examples.

• The filled Julia set. Fixed and periodic points.

• An introduction to the properties of the Fatou set and the Julia set.

• The Mandelbrot set: its definition and properties.

• Introduction to the iteration of transcendental entire functions.

• Similarities and differences between polynomials and transcendental entire functions.

• The escaping set: definition, properties, and its important role.

• Examples of the Fatou, Julia and escaping sets for transcendental entire functions.

Prerequisites

The lecture series will be addressed to PhD students of diverse mathematical backgrounds. We shall assume a basic knowledge of complex analysis and a little topology. Some more advanced background in complex analysis will be covered in the first lecture. No knowledge of dynamics will be assumed.

Registration

You can register anytime by emailing us at vasiliki.evdoridou@open.ac.uk. Once you are on the mailing list you will be receiving a link to join the online lecture on the Monday of that week.

Software

The lectures will be given on Microsoft Teams. Note that in order to attend you do not need to create an account. You can join the meeting through your browser using the link we will send you.

Lecturers: Vasiliki Evdoridou and Dave Sixsmith (The Open University)