The center-focus problem, Abelian integrals and the Hilbert's 16th problem.

• Grant number: 16/09269-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2016
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Matheus Manzatto de Castro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 12/18780-0 - Geometry of Control Systems, Dynamical and Stochastics Systems, AP.TEM

Abstract

In this project we propose a study about the center-focus problem for polynomial systems. After completing the classification of planar centers, the existence of limit cycles will be considered, together with their relations with the zeroes of Abelian integrals. We also study the proof of the weak version of the Hilbert's 16th problem (for systems of Bogdanov-Takens type).