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Cyclicity and local structural stability of piecewise vector fields

Grant number: 21/12630-5
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): May 01, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Regilene Delazari dos Santos Oliveira
Grantee:Ana Livia Rodero
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:19/21181-0 - New frontiers in Singularity Theory, AP.TEM
Associated scholarship(s):23/05686-0 - Integrability, center, and cyclicity problems for planar analytical vector fields, BE.EP.PD


The main goal of this project is the study of piecewise smooth vector fields defined in 2, 3 and 4-dimensional manifolds, in two distinct lines which will be addressed simultaneously. The goal of the first line of this project is to study the cyclicity problem for a system having multiple period rings, searching for an upper bound for the number of limit cycles that can bifurcate, simultaneously, of these rings. For the second line, we consider a piecewise smooth vector field Y=(X^+, X^-) defined in a 3-dimensional manifold. We would like to characterize the local structurally stable singularities for the system Y when we suppose that both X^+ and X^- are completely integrable and that Y is refractive. In the same context, we consider a piecewise-smooth refractive system Y defined in R^4 (under the hypoteses that X^+ and X^- are completely integrable and Y is refractive) and we would like to give initial answers about local stability and local bifurcations of codimension 1. (AU)

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