A WEIGHT-HOMOGENOUS CONDITION TO THE REAL JACOBIAN CONJECTURE IN R2

被引：4

作者：

Braun, Francisco ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

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

[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2021年 / 64卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Real Jacobian conjecture; global injectivity; weight-homogeneous polynomials; INJECTIVITY;

D O I：

10.1017/S0013091521000766

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that a polynomial local diffeomorphism (f, g) : R-2 -> R-2 is a global diffeomorphism provided the higher homogeneous terms of ff(x) + gg(x). and ff(y) + gg(y) do not have real linear factors in common. Here, we give a weight-homogeneous framework of this result. Our approach uses qualitative theory of differential equations. In our reasoning, we obtain a result on polynomial Hamiltonian vector fields in the plane, generalization of a known fact.

引用

页码：1028 / 1036

页数：9

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