Tuesday 29 Sep 2020: Dynamics Seminar: Complex dynamics: the intriguing case of wandering domains
Gwyneth Stallard - Open University
Complex dynamics concerns the iteration of analytic functions of the complex plane. For each function, the plane is split into two sets: the Fatou set (where the behaviour of the iterates is stable under local variation) and the Julia set (where the behaviour is chaotic). The dynamical behaviour of the iterates inside the periodic components of the Fatou set was classified into four different types by the founders of the subject and this classification has played a key role in the development of the subject. One of the most dramatic breakthroughs was given by Sullivan in the 1980s when he proved that, for rational functions, all components of the Fatou set are eventually periodic and there are no so-called wandering domains. For transcendental functions, however, wandering domains can exist and the rich variety of possible behaviours that can occur is only just becoming apparent.