Study of the center-focus problem in the nilpotent case

• Grant number: 24/23312-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2025
• End date: December 31, 2026
• 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: 23/02959-5 - Non-Smooth Systems and Singular Perturbations, AP.R

Abstract

Study of the Center-Focus Problem in Planar Analytic Differential Systems. Initially, to become familiar with the problem, we will study the case where the linear part is of the center type, which is due to Poincaré and Liapunov. Subsequently, the more challenging nilpotent case will be addressed. Additionally, an example of an orbitally symmetric nilpotent center will be sought, and a study of the local cyclicity of such centers will be conducted.