Mating Siegel and parabolic quadratic polynomials

Yuming Fu, Fei Yang

Let $f_{\theta }(z)=e^{2\pi i\theta }z+z^2$ be the quadratic polynomial having an indifferent fixed point at the origin. For any bounded type irrational number $\theta \in \mathbb{R}\setminus \mathbb{Q}$ a…