New classes of polynomial maps satisfying the real Jacobian conjecture in R-2

Author(s)

Itikawa, Jackson ^[1] ; Llibre, Jaume ^[2]

Affiliation

^[1] Univ Fed Rondonia, Dept Matemat, Campus BR 364, Km 9-5, BR-76801059 Porto Velho, RO - Brazil

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

• Document type: Journal article
• Source: Anais da Academia Brasileira de Ciências; v. 91, n. 2 2019.
• Web of Science Citations: 0

Abstract

We present two new classes of polynomial maps satisfying the real Jacobian conjecture in R-2. The first class is formed by the polynomials maps of the form (q(x)-p(y),q(y)+p(x)) : R-2 -> R-2 such that p and q are real polynomials satisfying p'(x)q'(x) not equal 0. The second class is formed by polynomials maps (f, g) : R-2 -> R-2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions. (AU)

• FAPESP's process: 16/23285-9 - On the real Jacobian conjecture and the center-type singularities
• Grantee: Jackson Itikawa
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor