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

Ewa Ligocka. "On complexification and iteration of quasiregular polynomials which have algebraic degree two." Fundamenta Mathematicae 186.3 (2005): 269-285. <http://eudml.org/doc/282706>.

@article{EwaLigocka2005,
abstract = {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.},
author = {Ewa Ligocka},
journal = {Fundamenta Mathematicae},
keywords = {iteration; polynomials; quasiregular},
language = {eng},
number = {3},
pages = {269-285},
title = {On complexification and iteration of quasiregular polynomials which have algebraic degree two},
url = {http://eudml.org/doc/282706},
volume = {186},
year = {2005},
}

TY - JOUR
AU - Ewa Ligocka
TI - On complexification and iteration of quasiregular polynomials which have algebraic degree two
JO - Fundamenta Mathematicae
PY - 2005
VL - 186
IS - 3
SP - 269
EP - 285
AB - 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.
LA - eng
KW - iteration; polynomials; quasiregular
UR - http://eudml.org/doc/282706
ER -