Introduce the student to the planar dynamic systems by studying the number of limit cycles that bifurcate from a linear center. In an initial phase, a study will be made on local aspects of the Qualitative Theory of Ordinary Differential Equations, with special emphasis on planar systems. In the sequence, a study of global aspects will be made, such as the notion of limit sets and attractors, Poincaré-Bendixon theorem and the Poincaré First Return Application in planar systems. In the final phase, the number of limit cycles that bifurcate from a linear center will be studied. As a preparation we will see the Poincaré-Melnikov integral method and the Abelian integral method. We will conclude the project by showing the upper limit of the number of cycles that branch from a linear center by a disturbance of degree n.
News published in Agência FAPESP Newsletter about the scholarship: