On complexification and iteration of quasiregular polynomials which have algebraic degree two

Abstract

We prove that each degree two quasiregular polynomial is conjugate to $Q(z)=z^{2}-(p+q)|z|^{2}+pq\overline{z}^{2}+c$, $|p|<1$, $|q|<1$. We also show that the complexification of $Q$ can be extended to a polynomial endomorphism of $\mathbb{C}\mathbb{P}^{2}