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

• Autorzy: Ewa Ligocka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 30C99: None of the above, but in this section
• 32H50: Iteration problems
• 30C62: Quasiconformal mappings in the plane
• 37F99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 3
• Strony: 269-285

Daty

wydano

2005

Twórcy

autor

Ewa Ligocka

• Institute of Mathematics, Department of Mathematics, Computer Science and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm186-3-5