On the complexification of real-analytic polynomial mappings of $\mathbb{R}^{2}$

Ewa Ligocka¹

¹ Institute of Mathematics Department of Mathematics, Computer Science and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland

Annales Polonici Mathematici, Tome 88 (2006) no. 2, pp. 119-125.

Résumé

We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from $\mathbb{R}^{2}$ into $\mathbb{R}^{2}$ which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of $\mathbb{C}\mathbb{P}^{2}$. We also prove that this extension acts on $\mathbb{C}\mathbb{P}^{2}\setminus\mathbb{C}^{2}$ as a quotient of finite Blaschke products.

Détail

DOI : 10.4064/ap88-2-3

Keywords: simple algebraic condition leading homogeneous term polynomial mapping mathbb mathbb which equivalent the complexification mapping extended polynomial endomorphism mathbb mathbb prove extension acts mathbb mathbb setminus mathbb quotient finite blaschke products