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Qualitative theory of ordinary differential equations: integrability, periodic orbits and phase portraits

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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VEICULO: TITULO (DATA)

Scientific publications (10)
(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 C.; OLIVEIRA, REGILENE D. S.; REZENDE, ALEX C. Structurally Unstable Quadratic Vector Fields of Codimension Two: Families Possessing Either a Cusp Point or Two Finite Saddle-Nodes. Journal of Dynamics and Differential Equations, v. 33, n. 4, p. 1779-1821, DEC 2021. Web of Science Citations: 3.
OLIVEIRA, REGILENE; REZENDE, ALEX C.; SCHLOMIUK, DANA; VULPE, NICOLAE. Characterization and bifurcation diagram of the family of quadratic differential systems with an invariant ellipse in terms of invariant polynomials. REVISTA MATEMATICA COMPLUTENSE, MAY 2021. Web of Science Citations: 0.
LLIBRE, JAUME; OLIVEIRA, REGILENE; ZHAO, YULIN. n the birth and death of algebraic limit cycles in quadratic differential system. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, v. 32, n. 2, p. 317-336, APR 2021. Web of Science Citations: 0.
MOTA, MARCOS C.; OLIVEIRA, REGILENE D. S. DYNAMIC ASPECTS OF SPROTT BC CHAOTIC SYSTEM. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 26, n. 3, p. 1653-1673, MAR 2021. Web of Science Citations: 0.
DIAS, F. S.; VALLS, CLAUDIA. Global dynamics of the Maxwell-Bloch system with invariant algebraic surfaces. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 35, n. 4, p. 668-681, OCT 1 2020. Web of Science Citations: 0.
DUKARIC, MASA; FERNANDES, WILKER; OLIVEIRA, REGILENE. Symmetric centers on planar cubic differential systems. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 197, AUG 2020. Web of Science Citations: 0.
OLIVEIRA, REGILENE; VALLS, CLAUDIA. GLOBAL DYNAMICS OF THE MAY-LEONARD SYSTEM WITH A DARBOUX INVARIANT. Electronic Journal of Differential Equations, JUN 3 2020. Web of Science Citations: 0.
OLIVEIRA, REGILENE; VALLS, CLAUDIA. ON THE ABEL DIFFERENTIAL EQUATIONS OF THIRD KIND. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 25, n. 5, p. 1821-1834, MAY 2020. Web of Science Citations: 0.
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.

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