Global injectivity of maps in R^n

• Grant number: 17/00136-0
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2017
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Francisco Braun
• Grantee: Francisco Braun
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated researchers: Bruna Orefice Okamoto ; Jaume Llibre Salo ; Jean Venato Santos ; José Ruidival Soares dos Santos Filho ; Luis Renato Gonçalves Dias

Abstract

Let F: R^n -> R^n be a C^infinity map such that its Jacobian determinant has no zeros. This project presents some directions in the investigation of additional conditions guarantying the global injectivity of F. We present two lines of research in case F is polynomial in R^2 and also a line of research in the general case. We intend to work with three main group of researchers. (AU)

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; DIAS, LUIS RENATO GONCALVES; VENATO-SANTOS, JEAN. A COUNTEREXAMPLE TO A CONJECTURE OF NOLLET AND XAVIER. Proceedings of the American Mathematical Society, v. 150, n. 4, p. 4-pg., 2022-04-01. (17/00136-0)

BRAUN, FRANCISCO; GONCALVES DIAS, LUIS RENATO; SANTOS, JEAN VENATO. ON GLOBAL INVERTIBILITY OF SEMI-ALGEBRAIC LOCAL DIFFEOMORPHISMS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 58, n. 2, p. 713-730, DEC 2021. (17/00136-0, 19/07316-0)

BRAUN, FRANCISCO; MEREU, ANA C.. Zero-Hopf bifurcation in a 3D jerk system. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 59, JUN 2021. (18/13481-0, 17/00136-0)

BRAUN, FRANCISCO; VALLS, CLAUDIA. A WEIGHT-HOMOGENOUS CONDITION TO THE REAL JACOBIAN CONJECTURE IN R-2. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 64, n. 4, p. 1028-1036, NOV 2021. (17/00136-0)

BRAUN, FRANCISCO; FERNANDES, FILIPE. New lower bounds for the maximal number of inseparable leaves of nonsingular polynomial foliations of the plane. Journal of Mathematical Analysis and Applications, v. 491, n. 1, NOV 1 2020. (17/00136-0)

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; DIAS, LUIS RENATO GONCALVES; VENATO-SANTOS, JEAN. ON TOPOLOGICAL APPROACHES TO THE JACOBIAN CONJECTURE IN DOUBLE-STRUCK CAPITAL C-N. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 63, n. 3, p. 10-pg., 2020-08-01. (17/00136-0)