Isochronous Centers on Center Manifolds

• Grant number: 24/16727-1
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2025
• End date: May 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cláudio Gomes Pessoa
• Grantee: Cláudio Gomes Pessoa
• 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

Abstract

In this project, our goal is to study isochronous centers on central manifolds of polynomial vector fields in R3. We will develop mathematical methods that allow the characterization of these centers according to the parameters of the system, avoiding, if possible, the direct restriction of the vector field to the finite expansion of a center manifold. Once characterized, we will focus on finding lower bounds for the number of limit cycles that bifurcate from these centers. (AU)