On nonsingular polynomial maps of ℝ²

Nguyen Van Chau, and Carlos Gutierrez. "On nonsingular polynomial maps of ℝ²." Annales Polonici Mathematici 88.3 (2006): 193-204. <http://eudml.org/doc/280387>.

@article{NguyenVanChau2006,
abstract = {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.},
author = {Nguyen Van Chau, Carlos Gutierrez},
journal = {Annales Polonici Mathematici},
keywords = {Jacobian conjecture; polynomial diffeomorphism},
language = {eng},
number = {3},
pages = {193-204},
title = {On nonsingular polynomial maps of ℝ²},
url = {http://eudml.org/doc/280387},
volume = {88},
year = {2006},
}

TY - JOUR
AU - Nguyen Van Chau
AU - Carlos Gutierrez
TI - On nonsingular polynomial maps of ℝ²
JO - Annales Polonici Mathematici
PY - 2006
VL - 88
IS - 3
SP - 193
EP - 204
AB - 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.
LA - eng
KW - Jacobian conjecture; polynomial diffeomorphism
UR - http://eudml.org/doc/280387
ER -