Hyperbolic Components and Wandering Domains in Complex Dynamics

Objective

Complex dynamics is a subfield of dynamical systems, where the systems in question are generated by the iteration of a holomorphic function on a complex manifold. This proposal concerns itself with the following question: What is the equivalent of a hyperbolic component for parameter families of entire functions with wandering domains? Both hyperbolicity and wandering domains are the subject of much research in the area, and lie at the core of some of the field's major open questions. This project attempts to link them by focusing on three separate objectives: - Investigating generalisations to wandering domains of the multiplier map, a central tool in understanding hyperbolic components for parameter families of rational functions. - Fully classifying the structure of the Teichmüller spaces associated to wandering domains of entire functions. - Obtaining quasiconformal invariants for the boundary dynamics of wandering domains.