Advanced search
Start date
Betweenand

Injectivity of polynomial maps in the plane

Grant number: 14/26149-3
Support Opportunities:Scholarships abroad - Research
Effective date (Start): September 01, 2015
Effective date (End): 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
Research place: 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.

News published in Agência FAPESP Newsletter about the scholarship:
Articles published in other media outlets (0 total):
More itemsLess items
VEICULO: TITULO (DATA)
VEICULO: TITULO (DATA)

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; TEIXEIRA, MARCO ANTONIO. Foliations, solvability, and global injectivity. ARCHIV DER MATHEMATIK, v. 119, n. 6, p. 17-pg., . (17/00136-0, 07/08231-0, 10/11323-7, 07/06896-5, 14/26149-3)
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., . (14/26149-3, 07/08231-0)
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, . (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. 256-265, . (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, . (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, . (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, . (14/26149-3, 12/18780-0)

Please report errors in scientific publications list using this form.