About the number of limit cycles that bifurcate from a linear center

• Grant number: 21/00193-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2021
• End date: January 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Nicolas Davi de Oliveira Deliberto
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM

Abstract

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.