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Qualitative Theory of Ordinary Differential Equations: integrability, periodic orbits and phase portraits

Grant number: 17/20854-5
Support type:Regular Research Grants
Duration: February 01, 2018 - February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Regilene Delazari dos Santos Oliveira
Grantee:Regilene Delazari dos Santos Oliveira
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil


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)

Scientific publications
(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)
LLIBRE, JAUME; OLIVEIRA, REGILENE D.; RODRIGUES, CAMILA AP B. Limit cycles for two classes of control piecewise linear differential systems. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, JAN 2020. Web of Science Citations: 0.
LLIBRE, JAUME; OLIVEIRA, REGILENE D. S.; VALLS, CLAUDIA. Final evolutions for simplified multistrain/two-stream model for tuberculosis and dengue fever. CHAOS SOLITONS & FRACTALS, v. 118, p. 181-186, JAN 2019. Web of Science Citations: 0.

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