On nonsingular polynomial maps of ℝ²

• Autorzy: Nguyen Van Chau , Carlos Gutierrez
• Języki publikacji: EN

Abstrakty

EN

We consider nonsingular polynomial maps F = (P,Q): ℝ² → ℝ² under the following regularity condition at infinity $(J_∞)$: There does not exist a sequence ${(p_k,q_k)} ⊂ ℂ²$ of complex singular points of F such that the imaginary parts $(ℑ(p_k),ℑ(q_k))$ tend to (0,0), the real parts $(ℜ(p_k),ℜ(q_k))$ tend to ∞ and $F(ℜ(p_k),ℜ(q_k))) → a ∈ ℝ²$. It is shown that F is a global diffeomorphism of ℝ² if it satisfies Condition $(J_∞)$ and if, in addition, the restriction of F to every real level set $P^{-1}(c)$ is proper for values of |c| large enough.

Kategorie tematyczne

• 14R15: Jacobian problem

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2006
• Tom: 88
• Numer: 3
• Strony: 193-204

Daty

wydano

2006

Twórcy

autor

Nguyen Van Chau

• Hanoi Institute of Mathematics, 18 Hoang Quoc Viet, Hanoi,Vietnam

autor

Carlos Gutierrez

• Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

Identyfikatory

DOI

10.4064/ap88-3-1