Geodesic
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

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
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

Ewa Ligocka 1

1 Institute of Mathematics Department of Mathematics, Computer Science and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland 
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Ewa Ligocka. On the complexification of real-analytic polynomial mappings of
$\mathbb{R}^{2}$. Annales Polonici Mathematici, Tome 88 (2006) no. 2, pp. 119-125. doi: 10.4064/ap88-2-3

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