Qualitative theory of differential equations and singularity theory
Injectivity of mappings and solvability for partial differentiable operators
Conformal Geometry applied to the problem of global injectivity
| Grant number: | 23/00376-2 |
| Support Opportunities: | Regular Research Grants |
| Start date: | May 01, 2023 |
| End date: | April 30, 2025 |
| 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 ; Filipe Balduino Pires Fernandes ; Jaume Llibre Salo ; Jean Venato Santos ; José Ruidival Soares dos Santos Filho ; Luis Renato Gonçalves Dias ; Nivaldo de Góes Grulha Júnior ; Thais Maria Dalbelo |
Abstract
Let F: R^n -> R^n be a local diffeomorphism. This project investigates additional conditions guaranteeing the global injectivity of F. The mechanisms of investigation are inside or are related to the area of dynamical systems, mainly concerning the qualitative theory of differential equations. We present three lines of research related to our projects along the last years with Brazilian and foreign collaborators. The first one deals with the polynomial case in R^2 and reach conditions related to the degree of F as well as the study of foliations of R^2 rising from polynomial submersions. The second one still deals with the polynomial case in R^2, but now under the viewpoint of the relations that the problem has with vector fields. Finally the third line of research deals with the n-dimensional situation, with n >= 3, in R^n and in C^n cases. (AU)
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