099 Ian Short

Ian Short (Open University, UK) // Iterated function systems in holomorphic dynamics // Abstract: Motivated by classical results in continued fraction theory, we explore iterated function systems of holomorphic self-maps of the disc and other Riemann surfaces. The primary tools in this endeavour are the hyperbolic metric and Pick's theorem that holomorphic maps are contractions of the hyperbolic metric. We will review selected results from this field over the last few decades and finish with work in preparation advancing these results by use of the hyperbolic derivative.