A WEIGHT-HOMOGENOUS CONDITION TO THE REAL JACOBIAN CONJECTURE IN R-2

Author(s)

Braun, Francisco ^[1] ; Valls, Claudia ^[2]

Affiliation

^[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

• Document type: Journal article
• Source: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 64, n. 4, p. 1028-1036, NOV 2021.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 17/00136-0 - Global injectivity of maps in R^n
• Grantee: Francisco Braun
• Support Opportunities: Regular Research Grants