Injectivity of polynomial maps in the plane

• Grant number: 14/26149-3
• Support Opportunities: Scholarships abroad - Research
• Start date: September 01, 2015
• End date: August 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Francisco Braun
• Grantee: Francisco Braun
• Host Investigator: Jaume Llibre
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain

Abstract

Let $F:\R^2\to\R^2$ be a polynomial map such that its Jacobian determinant does not have any zero. This project aims to investigate additional conditions that guarantee the global injectivity of $F$. Our main tool is the Qualitative Theory of Differential Equations. We intend to go deeper into researches already in progress, specially working with the connection between the problem of Global Injectivity and the study of centres of polynomial differential systems in the plane.

Scientific publications

(7)

(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)

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL. A correction to the paper ``Injective mappings and solvable vector fields of Euclidean spaces{''}. Topology and its Applications, v. 204, p. 256-265, MAY 15 2016. (14/26149-3, 07/08231-0)

ARTES, JOAN CARLES; BRAUN, FRANCISCO. The phase portrait of the Hamiltonian system associated to a Pinchuk map. Anais da Academia Brasileira de Ciências, v. 90, n. 3, p. 2599-2616, JUL-SEP 2018. (14/26149-3)

BRAUN, FRANCISCO; GINE, JAUME; LLIBRE, JAUME. A sufficient condition in order that the real Jacobian conjecture in R-2 holds. Journal of Differential Equations, v. 260, n. 6, p. 5250-5258, MAR 15 2016. (14/26149-3)

BRAUN, FRANCISCO; LLIBRE, JAUME; MEREU, ANA C.. ISOCHRONICITY FOR TRIVIAL QUINTIC AND SEPTIC PLANAR POLYNOMIAL HAMILTONIAN SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 36, n. 10, p. 5245-5255, OCT 2016. (14/26149-3, 12/18780-0)

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL; TEIXEIRA, MARCO ANTONIO. Foliations, solvability, and global injectivity. ARCHIV DER MATHEMATIK, v. 119, n. 6, p. 17-pg., 2022-10-11. (17/00136-0, 07/08231-0, 10/11323-7, 07/06896-5, 14/26149-3)

BRAUN, FRANCISCO; OREFICE-OKAMOTO, BRUNA. On polynomial submersions of degree 4 and the real Jacobian conjecture in R-2. Journal of Mathematical Analysis and Applications, v. 443, n. 2, p. 688-706, NOV 15 2016. (13/14014-3, 14/26149-3, 11/08877-3)

BRAUN, FRANCISCO; DOS SANTOS FILHO, JOSE RUIDIVAL. A correction to the paper "Injective mappings and solvable vector fields of Euclidean spaces". Topology and its Applications, v. 204, p. 10-pg., 2016-05-15. (14/26149-3, 07/08231-0)