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Injectivity of polynomial maps in the plane

Grant number: 14/26149-3
Support type: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 researcher:Francisco Braun
Grantee:Francisco Braun
Host: Jaume Llibre
Home 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.

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Scientific publications (5)
(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)
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. Web of Science Citations: 1.
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. Web of Science Citations: 1.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 2.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.