Renormalization for Siegel discs

This thesis investigates the existence of Siegel discs for iterated complex maps and looks at the properties of their boundary curves for golden mean rotation number. The key tool used is the idea of a renormalization operator acting on a space of functions. Firstly, a computer-assisted proof is discussed and verified, which establishes the existence of a fixed point of the relevant renormalization operator. In particular, the proof yields a ball of functions around an approximate fixed point that is guaranteed to contain the true fixed point. [Continues.]