On limit cycles that bifurcates from a center in a planar polynomial system.

• Grant number: 09/02989-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date until: September 01, 2009
• End date until: February 28, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Alex Carlucci Rezende
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 08/54222-6 - Singularities, geometry and differential equations, AP.TEM

Abstract

One of the most investigated problem in the qualitative theory of dynamical systems in the plane is the 16th Hilbert Problem dealing with limit cycles, more precisely the second part of the problem, which asks: What is the maximum number of limit cycles of a polynomial differential system of degree m?Limit cycle means an isolated closed orbit in the set of all orbits of a planar differential system. A classic way to obtain limit cycles is by perturbation of a system with a center singularity. There are 4 methods for the analysis of the number of limit cycles that bifurcate from a center. The main objective of this project is the study of such methods and their application to quadratic systems with rational integral.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

REZENDE, Alex Carlucci. Two methods for the investigation of limit cycles wich bifurcate from centers. 2011. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.