## Institute for Mathematical Sciences

## Preprint ims98-8

** M. Yampolsky and S. Zakeri**
* Mating Siegel Quadratic Polynomials*

Abstract: Let $F$ be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers $\theta$
and $\nu$. Using a new degree 3 Blaschke product model for the
dynamics of $F$ and an adaptation of complex a priori bounds
for renormalization of critical circle maps, we prove that $F$
can be realized as the mating of two Siegel quadratic
polynomials with the corresponding rotation numbers $\theta$
and $\nu$.

View ims98-8 (PDF format)