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

Grant number: 09/02989-4
Support type:Scholarships in Brazil - Master
Effective date (Start): September 01, 2009
Effective date (End): February 28, 2011
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Regilene Delazari dos Santos Oliveira
Grantee:Alex Carlucci Rezende
Home 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. Dois métodos para a investigação de ciclos limites que bifurcam de centros. 2011. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação São Carlos.

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