On nonsingular polynomial maps of $\mathbb R^2$

Tom 88 / 2006

Nguyen Van Chau, Carlos Gutierrez Annales Polonici Mathematici 88 (2006), 193-204 MSC: 14R15, 14E40. DOI: 10.4064/ap88-3-1

Streszczenie

We consider nonsingular polynomial maps $F = (P,Q):\mathbb R^2 \to \mathbb R^2$ under the following regularity condition at infinity $(J_\infty)$: There does not exist a sequence $\{(p_k,q_k)\}\subset \mathbb C^2$ of complex singular points of $F$ such that the imaginary parts $(\Im (p_k),\Im(q_k))$ tend to $(0,0)$, the real parts $(\Re(p_k), \Re(q_k))$ tend to $\infty$ and $F(\Re(p_k),\Re(q_k)) )\rightarrow a\in \mathbb R^2$. It is shown that $F$ is a global diffeomorphism of $\mathbb R^2$ if it satisfies Condition $(J_\infty)$ and if, in addition, the restriction of $F$ to every real level set $P^{-1}(c) $ is proper for values of $\vert c\vert$ large enough.

Autorzy

  • Nguyen Van ChauHanoi Institute of Mathematics
    18 Hoang Quoc Viet
    Hanoi,Vietnam
    e-mail
  • Carlos GutierrezDepartamento de Matemática
    ICMC–USP
    Caixa Postal 668
    13560–970, São Carlos, SP, Brazil
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek