On polynomial submersions of degree 4 and the real Jacobian conjecture in R2

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:443

Article

Braun, Francisco¹  Orefice-Okamoto, Bruna¹ 

[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

关键词: Real Jacobian conjecture;    Global injectivity;    Positive polynomials;    Half-Reeb components;   

DOI  :  10.1016/j.jmaa.2016.05.048

来源: Elsevier

【 摘 要 】

We prove the following version of the real Jacobian conjecture: Let F = (p, q) : R-2 -> R-2 be a polynomial map with nowhere zero Jacobian determinant. If the degree of p is less than or equal to 4, then F is injective. The approach to prove this result leads to a complete classification, up to affine change of coordinates, of the polynomial submersions of degree 4 in R-2 whose level sets are not all connected. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free