Geometry of Quadratic Julia Sets: A Transseries Approach
We introduce convergent transseries expansions for the B\"ottcher map near all periodic points on the Julia set of complex quadratic maps. These expansions allow us to study the geometric structure of the fractal. We will discuss the relation between transseries and important properties of Julia sets such as Holder continuity and the Hausdorff dimension. We will also show plots of fractals obtained by combining curve segments calculated using the transseries. They give direct insight into the intricate features of Julia sets.