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On nonsingular polynomial maps of ℝ²

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Chau N., Gutierrez C.

Annales Polonici Mathematici

2006

tom 88

nr 3

193-204

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Chau N.

1 Gutierrez C.

1 2006

Wyniki wyszukiwania

On nonsingular polynomial maps of ℝ²