The center-focus problem in cubic nilpotent and degenerate polynomial systems

• Grant number: 11/21898-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2012
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Regilene Delazari dos Santos Oliveira
• Grantee: Jackson Itikawa
• 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 classic problem in the qualitative theory of ordinary differential equations (ODE's) is the local planar singular point caracterization of vector systems. This problem is completely solved, except to the monodromic case, where the orbits turn around the singular point.In analytic differential systems, a monodromic singular point is either a center or a focus. The investigation that deals with the distinction between center and focus in such systems is called the center-focus problem. The problem can be divided in three cases: linear type (nondegenerate), nilpotent, and degenerate points.This project has the purpose of investigating nilpotent and degenerate centers in cubic and quartic differential systems.

Scientific publications

(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)

ITIKAWA, JACKSON; LLIBRE, JAUME. GLOBAL PHASE PORTRAITS OF UNIFORM ISOCHRONOUS CENTERS WITH QUARTIC HOMOGENEOUS POLYNOMIAL NONLINEARITIES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 1, p. 121-131, JAN 2016. (11/21898-0)