On the real Jacobian conjecture and the center-type singularities

• Grant number: 16/23285-9
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: February 01, 2017
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Jackson Itikawa
• Supervisor: Jaume Llibre Salo
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 15/07612-7 - Uniform isochronous centers in planar polynomial differential systems of degree 5, BP.PD

Abstract

Let F=(f,g) be a polynomial map with nonvanishing Jacobian determinant, such that F(0,0)=(0,0). This project aims to apply results from the dynamical systems theory in order to determine if there exists a counterexample to the real Jacobian conjecture with f and g of degree 5, which is so far the lower degree of a such counterexample could exist.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

JACKSON ITIKAWA; JAUME LLIBRE. New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. Anais da Academia Brasileira de Ciências, v. 91, n. 2, 2019-07-01. (16/23285-9)

ITIKAWA, JACKSON; LLIBRE, JAUME. New classes of polynomial maps satisfying the real Jacobian conjecture in R-2. Anais da Academia Brasileira de Ciências, v. 91, n. 2, 2019. (16/23285-9)