We prove that each degree two quasiregular polynomial is conjugate to Q(z) = z² - (p+q)|z|² + pqz̅² + c, |p| < 1, |q| < 1. We also show that the complexification of Q can be extended to a polynomial endomorphism of ℂℙ² which acts as a Blaschke product (z-p)/(1-p̅z) · (z-q)/(1-q̅z) on ℂℙ²∖ℂ². Using this fact we study the dynamics of Q under iteration.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-5,
author = {Ewa Ligocka},
title = {On complexification and iteration of quasiregular polynomials which have algebraic degree two},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {269-285},
zbl = {1087.30018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-5}
}
Ewa Ligocka. On complexification and iteration of quasiregular polynomials which have algebraic degree two. Fundamenta Mathematicae, Tome 185 (2005) pp. 269-285. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-5/