| Grant number: | 17/20854-5 |
| Support Opportunities: | Regular Research Grants |
| Start date: | February 01, 2018 |
| End date: | February 29, 2020 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Regilene Delazari dos Santos Oliveira |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Abstract
The main focus of this project is related with the existence of first integrals (A non constant and smooth functions a real values defined on open set $U$ of a manifold that is constant on the solution of the system). Using the knowlegde of distinct tools and diferent approaches we hope to contribute with the investigation on the global behavior of polynomial differential systens defined in the plane and in the space and, specially with the integrability of such systems in near future. Then, this project is linked with several subjects in the Real Dynamical Systems area and uses distinct mathematical tools. For instance the classification of the structurally unstable quadratic systems of codimension two modulo limit cycles, the classification of the quadratic systems possessing invariant algebraic conics, the investigation on center problem and linearizability problem, the global behavior of polynomial differential systems on R^3, the investigation of periodic orbits in smooth systems and piecewise systems with the averaging theory, among others. (AU)
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